Question

which is a true statement about an isosceles right triangle? a. the hypotenuse is $sqrt{3}$ times as long as either leg. b. the hypotenuse is $sqrt{2}$ times as long as either leg. c. each leg is $sqrt{2}$ times as long as the hypotenuse. d. each leg is $sqrt{3}$ times as long as the hypotenuse.

Explanation:

Step1: Recall Pythagorean theorem

Let the length of each leg of the isosceles right - triangle be $a$. By the Pythagorean theorem $c^{2}=a^{2}+a^{2}$, where $c$ is the hypotenuse.

Step2: Simplify the equation

$c^{2}=2a^{2}$. Then $c = \sqrt{2a^{2}}=\sqrt{2}a$.

Answer:

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