Question

nas figuras a seguir encontre as medidas x,y e z​

Answer 1

• Letra B

${x}^{2} = {12}^{2} + {9}^{2}$

${x}^{2} = 144 + 81$

$x = \sqrt{225}$

$\boxed{\red{x = 15}}$

____________________________

${18}^{2} = {15}^{2} + {y}^{2}$

$324 = 225 + {y}^{2}$

${y}^{2} = 99$

$y = \sqrt{99}$

$y = \sqrt{3 \times 3 \times 11}$

$\boxed{\red{y = 3 \sqrt{11} }}$

____________________________

$( {3 \sqrt{11}) }^{2} = {6}^{2} + {z}^{2}$

$9 \times 11 = 9 + {z}^{2}$

$99 = 9 + {z}^{2}$

${z}^{2} = 90$

$z = \sqrt{90}$

$z = \sqrt{3 \times 3 \times 10}$

$\boxed{\red{z = 3 \sqrt{10} }}$

• Letra C

${6}^{2} = {2}^{2} + {y}^{2}$

$36 = 4 + {y}^{2}$

${y}^{2} = 32$

$y = \sqrt{32}$

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

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

$\boxed{\red{y = 4 \sqrt{2} }}$

_____________________________

${x}^{2} = {12}^{2} + ( {4 \sqrt{2}) }^{2}$

${x}^{2} = 144 + 16 \times 2$

${x}^{2} = 144 + 32$

$x = \sqrt{176}$

$x = \sqrt{2 \times 2 \times 2 \times 2 \times 11}$

$x = 2 \times 2 \sqrt{11}$

$\boxed{\red{x = 4 \sqrt{11} }}$

• Letra D

${z}^{2} = {16}^{2} + {12}^{2}$

${z}^{2} = 256 + 144$

$z = \sqrt{400}$

$\boxed{\red{z = 20}}$

_________________________

${12}^{2} = 16 \times x$

$144 = 16x$

$x = \frac{144}{16}$

$\boxed{\red{x = 9}}$

_________________________

${y}^{2} = 9 \times 25$

${y}^{2} = 225$

$y = \sqrt{225}$

$\boxed{\red{y = 15}}$

Espero ter ajudado!