# If c is the measure of the hypotenuse of a right triangle, how do you find each missing measure given a=x, b=x+7, c=97?

Feb 26, 2017

$a = 65$ and $b = 72$.

#### Explanation:

By pythagorean theorem, we have

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

${x}^{2} + {\left(x + 7\right)}^{2} = {97}^{2}$

${x}^{2} + {x}^{2} + 14 x + 49 = 9409$

$2 {x}^{2} + 14 x - 9360 = 0$

${x}^{2} + 7 x - 4680 = 0$

$x = \frac{- 7 \pm \sqrt{{7}^{2} - 4 \cdot 1 \cdot - 4680}}{2 \cdot 1}$

$x = \frac{- 7 \pm 137}{2}$

$x = - 72 \mathmr{and} 65$

Obviously, a triangle with negative lengths is impossible. Therefore, we have that $a = 65$ and $b = 72$.

Hopefully this helps!