Find the leg and hypotenuse.

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.

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