Question

question 4 of 10 which is a true statement about a 45 - 45 - 90 triangle? a. the hypotenuse is $sqrt{3}$ times as long as either leg. b. each leg is $sqrt{3}$ times as long as the hypotenuse. c. each leg is $sqrt{2}$ times as long as the hypotenuse. d. the hypotenuse is $sqrt{2}$ times as long as either leg.

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

Let leg length be $a$. By Pythagorean theorem $c^{2}=a^{2}+a^{2}=2a^{2}$, so $c = \sqrt{2}a$ where $c$ is hypotenuse.

Answer:

D. The hypotenuse is $\sqrt{2}$ times as long as either leg.