Answer
In a $45^{\circ}-45^{\circ}$ right triangle, the hypotenuse has a length that is $\sqrt{2}$ times as long as either leg.
Work Step by Step
Two sides of a square and the diagonal across the square form a triangle with angles $45^{\circ}, 45^{\circ},$ and $90^{\circ}$.
The length of the three sides of the triangle can be expressed as $k, k,$ and $\sqrt{2}~k$.
In a $45^{\circ}-45^{\circ}$ right triangle, the hypotenuse has a length that is $\sqrt{2}$ times as long as either leg.
