Question

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

Explanation:

An isosceles right triangle has equal legs (length \(a\)) and a hypotenuse \(c\). By Pythagoras: \(c^2 = a^2 + a^2 = 2a^2\), so \(c = a\sqrt{2}\). Thus, hypotenuse is \(\sqrt{2}\) times a leg.

Answer:

A. The hypotenuse is \(\sqrt{2}\) times as long as either leg.