Question

if the hypotenuse of an isosceles right triangle has a length of 5 centimeters, what is the length of one of the legs?
select the correct answer.
$\frac{5}{2}$
5
$5\sqrt{2}$
$\frac{5\sqrt{2}}{2}$

Explanation:

Step1: Define variables for legs

Let each leg length be $x$ (isosceles right triangle, so legs are equal).

Step2: Apply Pythagorean theorem

$$x^2 + x^2 = 5^2$$

Step3: Simplify the equation

$$2x^2 = 25$$
$$x^2 = \frac{25}{2}$$

Step4: Solve for x

$$x = \sqrt{\frac{25}{2}} = \frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2}$$

Answer:

$\frac{5\sqrt{2}}{2}$ (matches the fourth option)