Question

Find the value of X! Please help!

Answer 1

ANSWER

$x = 8 \sqrt{3}$

EXPLANATION

${h}^{2} = {y}^{2} + {4}^{2}$
This implies that,

${h}^{2} = {y}^{2} + 16...eqn1$

Also,

${h}^{2} + {x}^{2} = {16}^{2} ...eqn2$

And

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

${y}^{2}={x}^{2} - 144 ...eqn3$

Put equation 1 into equation 2.

This will give us,

${y}^{2} + 16 + {x}^{2} = {16}^{2}$

${y}^{2} +{x}^{2} = {16}^{2} - 16$

${y}^{2} +{x}^{2} =16 ( 16 - 1)$

${y}^{2} +{x}^{2} =240...eqn4$

We put equation 3 into equation 4,

${x}^{2} - 144+{x}^{2} =240$

We simplify to get,

$2 {x}^{2} = 384$

${x}^{2} = 192$

$x = \sqrt{192}$

$x = 8 \sqrt{3}$