Question

an isosceles right triangle has legs of equal length. if the hypotenuse is 22 centimeters long, find the length of each leg
each leg is □ cm long.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

$x^2 + x^2 = 22^2$

Step2: Combine like terms

$2x^2 = 484$

Step3: Isolate $x^2$

$x^2 = \frac{484}{2} = 242$

Step4: Solve for $x$

$x = \sqrt{242} = \sqrt{121 \times 2} = 11\sqrt{2}$

Answer:

$11\sqrt{2}$