The hypotenuse of a $45°$-$45°$-$90°$ triangle measures $n$ in. What is the length of one leg of the triangle?

• A. $\frac{n}{\sqrt{2}}$ in.
• B. $\frac{n}{2}$ in.
• C. $n\times \sqrt{2}$ in.
• D. $n$ in.

Answer: (A)

Verified step by step guidance

1. Recognize that a 45°-45°-90° triangle is an isosceles right triangle, meaning the two legs are congruent and the angles opposite those legs are both 45°.
2. Recall the special side length ratios for a 45°-45°-90° triangle: if each leg has length \( x \), then the hypotenuse has length \( x \sqrt{2} \).
3. Set up the equation relating the hypotenuse \( n \) to the leg length \( x \): \( n = x \sqrt{2} \).
4. Solve for the leg length \( x \) by dividing both sides of the equation by \( \sqrt{2} \): \( x = \frac{n}{\sqrt{2}} \).
5. Conclude that the length of one leg of the triangle is \( \frac{n}{\sqrt{2}} \) inches.