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Berikut ini adalah pertanyaan dari anggawhite50 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Jawab menggunakan cara !​
Jawab menggunakan cara !​

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Nomor 1

Cari panjang AD terlebih dahulu

\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {60}^{o} &= \sf \frac{AD}{BD} \\ \sf \sqrt{3} &= \sf \frac{BC}{4 \: cm} \\ \sf AD &= \sf 4 \: cm \times \sqrt{3} \\ \sf AD &= \pink{\sf 4 \sqrt{3} \: cm} \end{aligned}}}

Maka, panjang AC adalah

\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {45}^{o} &= \sf \frac{AD}{AC} \\ \sf \frac{\sqrt{2}}{2} &= \sf \frac{4 \sqrt{3} \: cm}{AC} \\ \sf AC \times \sqrt{2} &= \sf 4 \sqrt{3} \: cm \times 2 \\ \sf AC \times \sqrt{2} &= \sf 8 \sqrt{3} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \times \frac{\sqrt{2}}{\sqrt{2}} \\ \sf AC &= \sf 4 \sqrt{6} \\ \sf AC &= \boxed{\pink{\sf 9,8 \: cm} \: \sf (Opsi \: b)} \end{aligned}}}

◌

Nomor 2

\boxed{\begin{aligned} \sf PR &= \sf \sqrt{{QR}^{2} - {PQ}^{2}} \\ \sf &= \sf \sqrt{{(29 \: cm)}^{{2}} - {(20 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{841 \: cm}^{{2}} - {400 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{441 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 21 \: cm} \: \sf (Opsi \: a)} \end{aligned}}

◌

Nomor 3

\boxed{\begin{aligned} \sf a &= \sf \sqrt{{(61)}^{{2}} - {(11)}^{{2}}} \\ \sf &= \sf \sqrt{3.721 - 121} \\ \sf &= \sf \sqrt{3.600} \\ \sf &= \sf \boxed{\pink{\sf 60} \: \sf (Opsi \: a)} \end{aligned}}

◌

Nomor 4

\boxed{\begin{aligned} \sf Jarak &= \sf \sqrt{((x_2 - x_1)^{2} + (y_2 - y_1)^{2})} \\ \sf &= \sf \sqrt{((4 - (- 3))^{2} + (-3 - 4)^{2})} \\ \sf &= \sf \sqrt{((4 + 3)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{((7)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{(49 + 49)} \\ \sf &= \boxed{\pink{\sf \sqrt{98} \: atau \: 7\sqrt{2}} \: \tiny{\sf (Tidak \: ada \: opsi)}} \end{aligned}}

◌

Nomor 5

Panjang PQ

\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {30}^{o} &= \sf \frac{PR}{PQ} \\ \sf \frac{\sqrt{3}}{3} &= \sf \frac{20 \: m}{PQ} \\ \sf PQ &= \sf \frac{20 \: m \times 3}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \: m}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \sqrt{3}}{3} \: m \\ \sf PQ &= \sf 20 \sqrt{3} \: m \\ \sf PQ &= \boxed{\pink{\sf 34,6\: m}} \end{aligned}}}

Panjang QR

\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {30}^{o} &= \sf \frac{PR}{QR} \\ \sf \frac{1}{2} &= \sf \frac{20 \: m}{QR} \\ \sf QR &= \sf 20 \: m \times 2 \\ \sf QR &= \boxed{\pink{\sf 40 \: m}} \end{aligned}}}

  • Jawaban: Opsi d

◌

Nomor 6

\small{\boxed{\begin{aligned} \sf Sisi \: Miring &= \sf \sqrt{{(20 \: cm)}^{2} + {(15 \: cm) }^{2}} \\ \sf &= \sf \sqrt{{400 \: cm}^{2} + {225 \: cm}^{2}} \\ \sf &= \sf \sqrt{{625 \: cm}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 25 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}

◌

Nomor 7

\small{\boxed{\begin{aligned} \sf Panjang &= \sf \sqrt{{Diagonal}^{2} - {Lebar}^{2}} \\ \sf &= \sf \sqrt{{(15 \: cm)}^{{2}} - {(9 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{225 \: cm}^{{2}} - {81 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{144 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 12 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}

◌

Nomor 8

Opsi d. Karena: \small{\red{\sf {6}^{2} + {8}^{2} = {10}^{2}}}

Penyelesaian:

\small{\boxed{\begin{aligned} \sf {(6\: cm)}^{2} + {(8 \: cm)}^{2} &..... \sf {(10 \: cm)}^{2} \\ \sf {36 \: cm}^{2} + {64 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &= \sf {100 \: cm}^{2} \\ \pink{\sf {(6\: cm)}^{2} + {(8 \: cm)}^{2}} & \pink{= \sf {(10 \: cm)}^{2}} \: \sf \: (Opsi \: d) \end{aligned}}}

◌

Nomor 9

\small{\boxed{\begin{aligned} \sf AC &= \sf \sqrt{{BC}^{2} - {AB}^{2}} \\ \sf &= \sf \sqrt{{(25 \: cm)}^{{2}} - {(7 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{625 \: cm}^{{2}} - {49 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{576 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 24 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}

◌

Nomor 10

\small{\boxed{\begin{aligned} \tiny{\sf Jarak \: terdekat} &= \sf \sqrt{{(600 \: km)}^{2} + {(800 \: km) }^{2}} \\ \sf &= \sf \sqrt{{360.000 \: km}^{2} + {640.000 \: km}^{2}} \\ \sf &= \sf \sqrt{{1.000.000 \: km}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 1.000 \: km}} \end{aligned}}}

Nomor 1Cari panjang AD terlebih dahulu[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {60}^{o} &= \sf \frac{AD}{BD} \\ \sf \sqrt{3} &= \sf \frac{BC}{4 \: cm} \\ \sf AD &= \sf 4 \: cm \times \sqrt{3} \\ \sf AD &= \pink{\sf 4 \sqrt{3} \: cm} \end{aligned}}}[/tex]Maka, panjang AC adalah[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {45}^{o} &= \sf \frac{AD}{AC} \\ \sf \frac{\sqrt{2}}{2} &= \sf \frac{4 \sqrt{3} \: cm}{AC} \\ \sf AC \times \sqrt{2} &= \sf 4 \sqrt{3} \: cm \times 2 \\ \sf AC \times \sqrt{2} &= \sf 8 \sqrt{3} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \times \frac{\sqrt{2}}{\sqrt{2}} \\ \sf AC &= \sf 4 \sqrt{6} \\ \sf AC &= \boxed{\pink{\sf 9,8 \: cm} \: \sf (Opsi \: b)} \end{aligned}}}[/tex]◌Nomor 2[tex]\boxed{\begin{aligned} \sf PR &= \sf \sqrt{{QR}^{2} - {PQ}^{2}} \\ \sf &= \sf \sqrt{{(29 \: cm)}^{{2}} - {(20 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{841 \: cm}^{{2}} - {400 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{441 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 21 \: cm} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 3[tex]\boxed{\begin{aligned} \sf a &= \sf \sqrt{{(61)}^{{2}} - {(11)}^{{2}}} \\ \sf &= \sf \sqrt{3.721 - 121} \\ \sf &= \sf \sqrt{3.600} \\ \sf &= \sf \boxed{\pink{\sf 60} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 4[tex]\boxed{\begin{aligned} \sf Jarak &= \sf \sqrt{((x_2 - x_1)^{2} + (y_2 - y_1)^{2})} \\ \sf &= \sf \sqrt{((4 - (- 3))^{2} + (-3 - 4)^{2})} \\ \sf &= \sf \sqrt{((4 + 3)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{((7)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{(49 + 49)} \\ \sf &= \boxed{\pink{\sf \sqrt{98} \: atau \: 7\sqrt{2}} \: \tiny{\sf (Tidak \: ada \: opsi)}} \end{aligned}}[/tex]◌Nomor 5Panjang PQ[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {30}^{o} &= \sf \frac{PR}{PQ} \\ \sf \frac{\sqrt{3}}{3} &= \sf \frac{20 \: m}{PQ} \\ \sf PQ &= \sf \frac{20 \: m \times 3}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \: m}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \sqrt{3}}{3} \: m \\ \sf PQ &= \sf 20 \sqrt{3} \: m \\ \sf PQ &= \boxed{\pink{\sf 34,6\: m}} \end{aligned}}}[/tex]Panjang QR[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {30}^{o} &= \sf \frac{PR}{QR} \\ \sf \frac{1}{2} &= \sf \frac{20 \: m}{QR} \\ \sf QR &= \sf 20 \: m \times 2 \\ \sf QR &= \boxed{\pink{\sf 40 \: m}} \end{aligned}}}[/tex]Jawaban: Opsi d◌Nomor 6[tex]\small{\boxed{\begin{aligned} \sf Sisi \: Miring &= \sf \sqrt{{(20 \: cm)}^{2} + {(15 \: cm) }^{2}} \\ \sf &= \sf \sqrt{{400 \: cm}^{2} + {225 \: cm}^{2}} \\ \sf &= \sf \sqrt{{625 \: cm}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 25 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 7[tex] \small{\boxed{\begin{aligned} \sf Panjang &= \sf \sqrt{{Diagonal}^{2} - {Lebar}^{2}} \\ \sf &= \sf \sqrt{{(15 \: cm)}^{{2}} - {(9 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{225 \: cm}^{{2}} - {81 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{144 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 12 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 8Opsi d. Karena: [tex] \small{\red{\sf {6}^{2} + {8}^{2} = {10}^{2}}} [/tex]Penyelesaian:[tex]\small{\boxed{\begin{aligned} \sf {(6\: cm)}^{2} + {(8 \: cm)}^{2} &..... \sf {(10 \: cm)}^{2} \\ \sf {36 \: cm}^{2} + {64 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &= \sf {100 \: cm}^{2} \\ \pink{\sf {(6\: cm)}^{2} + {(8 \: cm)}^{2}} & \pink{= \sf {(10 \: cm)}^{2}} \: \sf \: (Opsi \: d) \end{aligned}}}[/tex]◌Nomor 9[tex] \small{\boxed{\begin{aligned} \sf AC &= \sf \sqrt{{BC}^{2} - {AB}^{2}} \\ \sf &= \sf \sqrt{{(25 \: cm)}^{{2}} - {(7 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{625 \: cm}^{{2}} - {49 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{576 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 24 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 10[tex]\small{\boxed{\begin{aligned} \tiny{\sf Jarak \: terdekat} &= \sf \sqrt{{(600 \: km)}^{2} + {(800 \: km) }^{2}} \\ \sf &= \sf \sqrt{{360.000 \: km}^{2} + {640.000 \: km}^{2}} \\ \sf &= \sf \sqrt{{1.000.000 \: km}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 1.000 \: km}} \end{aligned}}}[/tex]Nomor 1Cari panjang AD terlebih dahulu[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {60}^{o} &= \sf \frac{AD}{BD} \\ \sf \sqrt{3} &= \sf \frac{BC}{4 \: cm} \\ \sf AD &= \sf 4 \: cm \times \sqrt{3} \\ \sf AD &= \pink{\sf 4 \sqrt{3} \: cm} \end{aligned}}}[/tex]Maka, panjang AC adalah[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {45}^{o} &= \sf \frac{AD}{AC} \\ \sf \frac{\sqrt{2}}{2} &= \sf \frac{4 \sqrt{3} \: cm}{AC} \\ \sf AC \times \sqrt{2} &= \sf 4 \sqrt{3} \: cm \times 2 \\ \sf AC \times \sqrt{2} &= \sf 8 \sqrt{3} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \times \frac{\sqrt{2}}{\sqrt{2}} \\ \sf AC &= \sf 4 \sqrt{6} \\ \sf AC &= \boxed{\pink{\sf 9,8 \: cm} \: \sf (Opsi \: b)} \end{aligned}}}[/tex]◌Nomor 2[tex]\boxed{\begin{aligned} \sf PR &= \sf \sqrt{{QR}^{2} - {PQ}^{2}} \\ \sf &= \sf \sqrt{{(29 \: cm)}^{{2}} - {(20 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{841 \: cm}^{{2}} - {400 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{441 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 21 \: cm} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 3[tex]\boxed{\begin{aligned} \sf a &= \sf \sqrt{{(61)}^{{2}} - {(11)}^{{2}}} \\ \sf &= \sf \sqrt{3.721 - 121} \\ \sf &= \sf \sqrt{3.600} \\ \sf &= \sf \boxed{\pink{\sf 60} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 4[tex]\boxed{\begin{aligned} \sf Jarak &= \sf \sqrt{((x_2 - x_1)^{2} + (y_2 - y_1)^{2})} \\ \sf &= \sf \sqrt{((4 - (- 3))^{2} + (-3 - 4)^{2})} \\ \sf &= \sf \sqrt{((4 + 3)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{((7)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{(49 + 49)} \\ \sf &= \boxed{\pink{\sf \sqrt{98} \: atau \: 7\sqrt{2}} \: \tiny{\sf (Tidak \: ada \: opsi)}} \end{aligned}}[/tex]◌Nomor 5Panjang PQ[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {30}^{o} &= \sf \frac{PR}{PQ} \\ \sf \frac{\sqrt{3}}{3} &= \sf \frac{20 \: m}{PQ} \\ \sf PQ &= \sf \frac{20 \: m \times 3}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \: m}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \sqrt{3}}{3} \: m \\ \sf PQ &= \sf 20 \sqrt{3} \: m \\ \sf PQ &= \boxed{\pink{\sf 34,6\: m}} \end{aligned}}}[/tex]Panjang QR[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {30}^{o} &= \sf \frac{PR}{QR} \\ \sf \frac{1}{2} &= \sf \frac{20 \: m}{QR} \\ \sf QR &= \sf 20 \: m \times 2 \\ \sf QR &= \boxed{\pink{\sf 40 \: m}} \end{aligned}}}[/tex]Jawaban: Opsi d◌Nomor 6[tex]\small{\boxed{\begin{aligned} \sf Sisi \: Miring &= \sf \sqrt{{(20 \: cm)}^{2} + {(15 \: cm) }^{2}} \\ \sf &= \sf \sqrt{{400 \: cm}^{2} + {225 \: cm}^{2}} \\ \sf &= \sf \sqrt{{625 \: cm}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 25 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 7[tex] \small{\boxed{\begin{aligned} \sf Panjang &= \sf \sqrt{{Diagonal}^{2} - {Lebar}^{2}} \\ \sf &= \sf \sqrt{{(15 \: cm)}^{{2}} - {(9 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{225 \: cm}^{{2}} - {81 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{144 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 12 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 8Opsi d. Karena: [tex] \small{\red{\sf {6}^{2} + {8}^{2} = {10}^{2}}} [/tex]Penyelesaian:[tex]\small{\boxed{\begin{aligned} \sf {(6\: cm)}^{2} + {(8 \: cm)}^{2} &..... \sf {(10 \: cm)}^{2} \\ \sf {36 \: cm}^{2} + {64 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &= \sf {100 \: cm}^{2} \\ \pink{\sf {(6\: cm)}^{2} + {(8 \: cm)}^{2}} & \pink{= \sf {(10 \: cm)}^{2}} \: \sf \: (Opsi \: d) \end{aligned}}}[/tex]◌Nomor 9[tex] \small{\boxed{\begin{aligned} \sf AC &= \sf \sqrt{{BC}^{2} - {AB}^{2}} \\ \sf &= \sf \sqrt{{(25 \: cm)}^{{2}} - {(7 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{625 \: cm}^{{2}} - {49 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{576 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 24 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 10[tex]\small{\boxed{\begin{aligned} \tiny{\sf Jarak \: terdekat} &= \sf \sqrt{{(600 \: km)}^{2} + {(800 \: km) }^{2}} \\ \sf &= \sf \sqrt{{360.000 \: km}^{2} + {640.000 \: km}^{2}} \\ \sf &= \sf \sqrt{{1.000.000 \: km}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 1.000 \: km}} \end{aligned}}}[/tex]Nomor 1Cari panjang AD terlebih dahulu[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {60}^{o} &= \sf \frac{AD}{BD} \\ \sf \sqrt{3} &= \sf \frac{BC}{4 \: cm} \\ \sf AD &= \sf 4 \: cm \times \sqrt{3} \\ \sf AD &= \pink{\sf 4 \sqrt{3} \: cm} \end{aligned}}}[/tex]Maka, panjang AC adalah[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {45}^{o} &= \sf \frac{AD}{AC} \\ \sf \frac{\sqrt{2}}{2} &= \sf \frac{4 \sqrt{3} \: cm}{AC} \\ \sf AC \times \sqrt{2} &= \sf 4 \sqrt{3} \: cm \times 2 \\ \sf AC \times \sqrt{2} &= \sf 8 \sqrt{3} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \\ \sf AC &= \sf \frac{8 \sqrt{3}}{\sqrt{2}} \: cm \times \frac{\sqrt{2}}{\sqrt{2}} \\ \sf AC &= \sf 4 \sqrt{6} \\ \sf AC &= \boxed{\pink{\sf 9,8 \: cm} \: \sf (Opsi \: b)} \end{aligned}}}[/tex]◌Nomor 2[tex]\boxed{\begin{aligned} \sf PR &= \sf \sqrt{{QR}^{2} - {PQ}^{2}} \\ \sf &= \sf \sqrt{{(29 \: cm)}^{{2}} - {(20 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{841 \: cm}^{{2}} - {400 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{441 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 21 \: cm} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 3[tex]\boxed{\begin{aligned} \sf a &= \sf \sqrt{{(61)}^{{2}} - {(11)}^{{2}}} \\ \sf &= \sf \sqrt{3.721 - 121} \\ \sf &= \sf \sqrt{3.600} \\ \sf &= \sf \boxed{\pink{\sf 60} \: \sf (Opsi \: a)} \end{aligned}}[/tex]◌Nomor 4[tex]\boxed{\begin{aligned} \sf Jarak &= \sf \sqrt{((x_2 - x_1)^{2} + (y_2 - y_1)^{2})} \\ \sf &= \sf \sqrt{((4 - (- 3))^{2} + (-3 - 4)^{2})} \\ \sf &= \sf \sqrt{((4 + 3)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{((7)^{2} + (-7)^{2})} \\ \sf &= \sf \sqrt{(49 + 49)} \\ \sf &= \boxed{\pink{\sf \sqrt{98} \: atau \: 7\sqrt{2}} \: \tiny{\sf (Tidak \: ada \: opsi)}} \end{aligned}}[/tex]◌Nomor 5Panjang PQ[tex]\small{\boxed{ \begin{aligned} \sf Tan \: \alpha &= \sf \frac{De}{Sa} \\ \sf Tan \: {30}^{o} &= \sf \frac{PR}{PQ} \\ \sf \frac{\sqrt{3}}{3} &= \sf \frac{20 \: m}{PQ} \\ \sf PQ &= \sf \frac{20 \: m \times 3}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \: m}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \\ \sf PQ &= \sf \frac{60 \sqrt{3}}{3} \: m \\ \sf PQ &= \sf 20 \sqrt{3} \: m \\ \sf PQ &= \boxed{\pink{\sf 34,6\: m}} \end{aligned}}}[/tex]Panjang QR[tex]\small{\boxed{ \begin{aligned} \sf Sin \: \alpha &= \sf \frac{De}{Mi} \\ \sf Sin \: {30}^{o} &= \sf \frac{PR}{QR} \\ \sf \frac{1}{2} &= \sf \frac{20 \: m}{QR} \\ \sf QR &= \sf 20 \: m \times 2 \\ \sf QR &= \boxed{\pink{\sf 40 \: m}} \end{aligned}}}[/tex]Jawaban: Opsi d◌Nomor 6[tex]\small{\boxed{\begin{aligned} \sf Sisi \: Miring &= \sf \sqrt{{(20 \: cm)}^{2} + {(15 \: cm) }^{2}} \\ \sf &= \sf \sqrt{{400 \: cm}^{2} + {225 \: cm}^{2}} \\ \sf &= \sf \sqrt{{625 \: cm}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 25 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 7[tex] \small{\boxed{\begin{aligned} \sf Panjang &= \sf \sqrt{{Diagonal}^{2} - {Lebar}^{2}} \\ \sf &= \sf \sqrt{{(15 \: cm)}^{{2}} - {(9 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{225 \: cm}^{{2}} - {81 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{144 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 12 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 8Opsi d. Karena: [tex] \small{\red{\sf {6}^{2} + {8}^{2} = {10}^{2}}} [/tex]Penyelesaian:[tex]\small{\boxed{\begin{aligned} \sf {(6\: cm)}^{2} + {(8 \: cm)}^{2} &..... \sf {(10 \: cm)}^{2} \\ \sf {36 \: cm}^{2} + {64 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &..... \sf {100 \: cm}^{2} \\ \sf {100 \: cm}^{2} &= \sf {100 \: cm}^{2} \\ \pink{\sf {(6\: cm)}^{2} + {(8 \: cm)}^{2}} & \pink{= \sf {(10 \: cm)}^{2}} \: \sf \: (Opsi \: d) \end{aligned}}}[/tex]◌Nomor 9[tex] \small{\boxed{\begin{aligned} \sf AC &= \sf \sqrt{{BC}^{2} - {AB}^{2}} \\ \sf &= \sf \sqrt{{(25 \: cm)}^{{2}} - {(7 \: cm)}^{{2}}} \\ \sf &= \sf \sqrt{{625 \: cm}^{{2}} - {49 \: cm}^{{2}}} \\ \sf &= \sf \sqrt{{576 \: cm}^{{2}}} \\ \sf &= \sf \boxed{\pink{\sf 24 \: cm} \: \sf (Opsi \: c)} \end{aligned}}}[/tex]◌Nomor 10[tex]\small{\boxed{\begin{aligned} \tiny{\sf Jarak \: terdekat} &= \sf \sqrt{{(600 \: km)}^{2} + {(800 \: km) }^{2}} \\ \sf &= \sf \sqrt{{360.000 \: km}^{2} + {640.000 \: km}^{2}} \\ \sf &= \sf \sqrt{{1.000.000 \: km}^{2}} \\ \sf &= \sf \boxed{\pink{\sf 1.000 \: km}} \end{aligned}}}[/tex]

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Last Update: Thu, 28 Apr 22
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