Question

the hypotenuse of a 45 - 45 - 90 triangle measures 22\sqrt{2} units. what is the length of one leg of the triangle? 11 units 11\sqrt{2} units 22 units 22\sqrt{2} units

Explanation:

Step1: Recall ratio for 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the length of a leg $a$ to the hypotenuse $c$ is $a:c = 1:\sqrt{2}$, or $c = a\sqrt{2}$.

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