## Geometry: Common Core (15th Edition)

$x = 15$ $y = 15$
In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, we know that the hypotenuse is $\sqrt 2$ times each leg. Let's write an equation to solve for $x$, the length of a leg: $15 \sqrt 2 = \sqrt 2(x)$ Divide each side by $\sqrt 2$ to solve for $x$: $x = 15$ We know that in this type of triangle, the legs are equal to one another. Since one leg, $x$, measures $15$, the other leg, $y$, also equals $15$.