Question

Which of the following statements is true about a 45°-45° right triangle with congruent legs?

A) The length of the hypotenuse is equal to the length of a leg multiplied by the square root of 2
B) The length of the hypotenuse is equal to the length of a leg multiplied by the square root of 3
C) The length of tre hypotenuse is equal to the squared value of the length of one leg.
D) The length of the hypotenuse is equal to the cubed value of the length of one leg.

Answer 1

A) The length of the hypotenuse is equal to the length of a leg multiplied by the square root of 2

Explanation:

Let the leg length of the triangle be represented by x. The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse. If c represents the length of the hypotenuse, we have ...

x² +x² = c²

2x² = c²

c = √(2x²) = (√2)x

The length of the hypotenuse is √2 times the leg length.