Two legs of a right triangle are two consecutive even integers while the hypotenuse is 10 inches. What are the measure of both legs?

Mar 23, 2018

6 inches and 8 inches

Explanation:

We know that ${a}^{2} + {b}^{2} = {c}^{2}$
Let $a = x$, $b = x + 2$, $c = 10$
${x}^{2} + {\left(x + 2\right)}^{2} = {10}^{2}$
${x}^{2} + {x}^{2} + 4 x + 4 = 100$
$2 {x}^{2} + 4 x + 4 = 100$
${x}^{2} + 2 x + 2 = 50$
${x}^{2} + 2 x - 48 = 0$
$\left(x - 6\right) \left(x + 8\right) = 0$
$x = 6 \mathmr{and} x = - 8$
$x = 6$ (can't be negative)
$x + 2 = 8$
$a = 6 , b = 8$