Answer:
Hypotenuse length is (√2)x if the leg lengths are x and x respectively.
Step-by-step explanation:
This is an isosceles right triangle. The two acute angles are 45 degrees each and the leg lengths can be represented by x. Applying the Pythagorean Theorem, we get x^2 + x^2 = h^2 (where h is the length of the hypotenuse), or
2x^2 = h^2.
Solve this for h. Taking the square root of both sides of this equation, we get:
(√2)x = h
Conclusion: if the two legs of this equilateral right triangle are x and x, respectively, the length of the hypotenuse is h = √2x.
