#### Answer

In a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg

#### Work Step by Step

1. Draw a square with sides equal to k
2. Draw diagonals and label them as c. The diagonal forms two isosceles right triangles. Each angle formed by a side of the square and the diagonal measures $45^{\circ}$
3. Using the Pythagorean theorem express c (length of the diagonal)
$k^{2}+k^{2}=c^{2}$
$2k^{2} = c^{2}$
$c= \sqrt {2k^{2}}$
$c= k\sqrt {2}$
Therefore, in a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg