Question

this is a 45-45-90 triangle. what is the measure of x? √13 x x = √?

Explanation:

Step1: Identify 45-45-90 triangle properties

Legs are equal; hypotenuse = leg×√2. Given hypotenuse = √13.

Step2: Solve for leg length x

x = hypotenuse / √2 = √13 / √2 = √(26)/2? No, wait: x² + x² = (√13)² → 2x²=13 → x²=13/2 → x=√(13/2)? No, wait the question says x=√[?], so x²=13/2? No, no—wait the triangle: the labeled side is √13, if it's a leg (since it's a 45-45-90, legs are equal). Wait no, the right angle is marked, so the two legs are equal. If one leg is √13, then the other leg x is also √13? Wait no, wait the hypotenuse is opposite right angle. Wait the diagram: the right angle is at the bottom left, so the two legs are the sides forming the right angle, and the hypotenuse is the other side. If the side labeled √13 is a leg, then x (the other leg) is equal to √13, so x=√13, so the box is 13. Oh, yes—45-45-90 triangles have equal legs. So if one leg is √13, the other leg x is √13, so x=√13, so the value inside the square root is 13.

Answer:

13