# Consider a rectangle with a diagonal drawn between two vertices. Two right triangles are formed, each with one leg 5 inches longer than the other. The diagonal measure 25 inches. What do the legs measure?

Oct 13, 2016

Since a rectangle is a two dimensional shape with four right angles, we can apply pythagorean theorem.

Let $x$ be the length of the shorter leg and $x + 5$ be the length of the longer leg.

${x}^{2} + {\left(x + 5\right)}^{2} = {25}^{2}$

${x}^{2} + {x}^{2} + 10 x + 25 = 625$

$2 {x}^{2} + 10 x - 600 = 0$

$2 \left({x}^{2} + 5 x - 300\right) = 0$

$x = \frac{- 5 \pm \sqrt{{5}^{2} - 4 \times 1 \times - 300}}{2 \times 1}$

$x = \frac{- 5 \pm 35}{2}$

$x = \frac{30}{2} \mathmr{and} - \frac{40}{2}$

$x = 15 \mathmr{and} - 20$

A negative answer for a leg of a triangle is not possible, so the legs measure $15$ and $20$ inches.

Hopefully this helps!