# If c is the measure of the hypotenuse of a right triangle, how do you find each missing measure given a=8, b=x, c=x+2?

Apr 18, 2017

$c = 17$
$b = 15$

#### Explanation:

Apply Pythagorean theorem ${a}^{2} + {b}^{2} = {c}^{2}$

$b = x$ and $c = x + 2$

${8}^{2} + {x}^{2} = {\left(x + 2\right)}^{2}$

${8}^{2} + {x}^{2} = \left(x + 2\right) \left(x + 2\right)$

${8}^{2} + {x}^{2} = {x}^{2} + 4 x + 4$

${8}^{2} = 4 x + 4$

$64 = 4 x + 4$

$60 = 4 x$

$x = 15$

$c = x + 2$
$c = 15 + 2$
$\textcolor{red}{c = 17}$

$b = x$
$\textcolor{red}{b = 15}$