# Andrew claims that a wooden bookend in the shape of a 45°- 45°- 90° right triangle has side lengths of 9 in., 9 in., and 11 in. Is he correct?

Nov 6, 2015

No; if the sides of the right angle are 9 in. long each, then the hypotenuse would need to be over 12 in.

#### Explanation:

According to the Pythagorean Theorem
for a right triangle with sides $a , b , c$ where $c$ is the hypotenuse
$\textcolor{w h i t e}{\text{XXX}} c = \sqrt{{a}^{2} + {b}^{2}}$

For the given non-hypotenuse sides:
$\textcolor{w h i t e}{\text{XXX}} c = \sqrt{{9}^{2} + {9}^{2}} = \sqrt{162} \cong 12.73$

but Andrew claims $c = 11$