An isosceles right triangle has legs of equal length. if the hypotenuse is 22 inches long, find the length of each leg. i need an answer to this math problem so ! : (

15.56 inches

Let L represent the leg length. Then the Pythagorean theorem tells you ...

... 22² = L² + L² . . . . the square of the hypotenuse is the sum of the squares of the other two sides

... 484 = 2L² . . . . . . . simplify

... 242 = L² . . . . . . . . divide by 2; next, take the square root

... √242 = L ≈ 15.56 . . . . inches

Comment on this problem in general

For a hypotenuse of length H, the above equation becomes ...

... H² = L² +L² = 2L²

... H²/2 = L² . . . . . divide by 2

... H/√2 = L . . . . . take the square root (general solution for isosceles right triangles)

For your problem, this is ...

... (22 in)/1.414214 = L = 15.556 in

answer: 40.95

step-by-step explanation:

this answer is !