Question

the hypotenuse of a 45° - 45° - 90° triangle measures 22√2 units. what is the length of one leg of the triangle? 11 units 11√2 units 22 units 22√2 units

Explanation:

Step1: Recall ratio for 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, if the length of a leg is $a$, the length of the hypotenuse $c$ is $c = a\sqrt{2}$.

Step2: Solve for the leg length

Given $c = 22\sqrt{2}$, and $c=a\sqrt{2}$. Then $a\sqrt{2}=22\sqrt{2}$. Divide both sides by $\sqrt{2}$, we get $a = 22$.

Answer:

C. 22 units