Question

if a $45^\circ$-$45^\circ$-$90^\circ$ triangle has a hypotenuse length of $7\sqrt{2}$, what is the length of each leg of the triangle?
select the correct answer.
$7\sqrt{2}$
7
$\sqrt{2}$
2

Explanation:

Step1: Define leg length variable

Let each leg length be $x$.

Step2: Apply Pythagorean theorem

$$x^2 + x^2 = (7\sqrt{2})^2$$

Step3: Simplify both sides

$$2x^2 = 49 \times 2$$

Step4: Solve for $x^2$

$$x^2 = 49$$

Step5: Find positive root for length

$$x = \sqrt{49} = 7$$

Answer:

7