Question

Aplique o teorema de Pitágoras e determine o valor de x ​

Answer 1

Resposta:

$a) \: x = 2 \: e \: y = 15 \sqrt{2}$

$b) \: x = 6$

Explicação passo-a-passo:

a)

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

P/ achar o x:

${x}^{2} = {15}^{2} + {20}^{2}$

${x}^{2} = 225 + 400$

${x}^{2} = 625$

$x = \sqrt{625}$

x = 25

P/ achar o y:

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

${25}^{2} = {(5 \sqrt{7}) }^{2} + {y}^{2}$

$625 = (25 \times 7) + {y}^{2}$

$625 = 175 + {y}^{2}$

$625 - 175 = {y}^{2}$

$450 = {y}^{2}$

$\sqrt{450} = y$

Fatorando 450, temos

450 | 2

225 | 3

75 | 3

25 | 5

5 | 5

1 | ( 450= 2 x 3 x 3 x 5 x 5 )

Voltando à conta:

$\sqrt{450} = y$

$\sqrt{2 \times {3}^{2} \times {5}^{2} } = y$

$3 \times 5 \sqrt{2} = y$

$15 \sqrt{2} = y$

$y =15 \sqrt{2}$

b)

${10}^{2} = {8}^{2} + {x}^{2}$

$100 = 64 \times {x}^{2}$

$100 - 64 = {x}^{2}$

$36 = {x}^{2}$

$\sqrt{36} = x$

$6 = x$

x=6