Question

TEOREMA DE PITÁGORAS
Alguém poderia me ajudar nessas questões.

Answer 1

Resposta:

Teorema de Pitágoras:

${a}^{2} = {b}^{2} + {c}^{2}$

Explicação passo-a-passo:

A)

${x}^{2} = {10}^{2} + {6}^{2} \\ {x}^{2} = 100 + 36 \\ x = \sqrt{136} = 2 \sqrt{34}$

B)

${11}^{2} = {5}^{2} + {x}^{2} \\ 121 = 25 + {x}^{2} \\ {x}^{2} = 96 \\ x = \sqrt{96} = 4 \sqrt{6}$

C)

${x}^{2} = {2}^{2} + {9}^{2} \\ {x}^{2} = 4 + 81 \\ {x}^{2} = 85 \\ x = \sqrt{85}$

D)

${x}^{2} = {7}^{2} + {5}^{2} \\ {x}^{2} = 49 + 25 \\ {x}^{2} = 74 \\ x = \sqrt{74}$

E)

${20}^{2} = {(3x)}^{2} + {(4x)}^{2} \\ 400 = 9 {x}^{2} + 16 {x}^{2} \\ 400 = 25 {x}^{2} \\ \frac{400}{25} = {x}^{2} \\ {x}^{2} = 16 \\ x = \sqrt{16} = 4$

F)

${10}^{2} = {x}^{2} + {x}^{2} \\ 100 = 2 {x}^{2} \\ \frac{100}{2} = {x}^{2} \\ {x}^{2} = 50 \\ x = \sqrt{50} = 5 \sqrt{2}$

G)

${(6 \sqrt{7)} }^{2} = {8}^{2} + {x}^{2} \\ 36 \times 7 = 64 + {x}^{2} \\ 252 - 64 = {x}^{2} \\ 188 = {x}^{2} \\ x = \sqrt{188} = 2 \sqrt{47}$

H)

${(2x)}^{2} = {x}^{2} + {(5 \sqrt{2}) }^{2} \\ 4 {x}^{2} - {x}^{2} = 25 \times 2 \\ 3 {x}^{2} = 50 \\ x = \sqrt{ \frac{50}{3} } = \frac{5 \sqrt{6} }{3}$

I)

${x}^{2} = {( \sqrt{5)} }^{2} + {( \sqrt{7}) }^{2} \\ {x}^{2} = 5 + 7 \\ x = \sqrt{12} = 2 \sqrt{3}$

J)

${x}^{2} = {( \sqrt{8}) }^{2} + {(3 \sqrt{2})}^{2} \\ {x}^{2} = 8 + 9 \times 2 \\ {x}^{2} = 8 + 18 \\ x = \sqrt{26}$

Espero ter ajudado