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 45-45-90 triangle ratio

For a 45°-45°-90° triangle, hypotenuse $= \text{leg} \times \sqrt{2}$, so $\text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}}$.

Step2: Substitute hypotenuse value

Substitute hypotenuse $= 22\sqrt{2}$:
$\text{leg} = \frac{22\sqrt{2}}{\sqrt{2}}$

Step3: Simplify the expression

The $\sqrt{2}$ terms cancel out:
$\text{leg} = 22$

Answer:

22 units (Option C)