Question

the hypotenuse of a 45° - 45° - 90° triangle measures 7\sqrt{2} units. what is the length of one leg of the triangle? o 7 units o 7\sqrt{2} units o 14 units o 14\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 $c = 7\sqrt{2}$, and $c=a\sqrt{2}$. Then $a\sqrt{2}=7\sqrt{2}$. Divide both sides by $\sqrt{2}$, we get $a = 7$.

Answer:

A. 7 units