Find X in Isosceles Right Triangle ABC with Hypotenuse 60

To solve this problem, we need to determine the length of side $X$ in the right isosceles triangle $\triangle ABC$ with the hypotenuse $\sqrt{50}$.

• Step 1: Recall the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse. For this isosceles case, where both legs $X$ are equal:
$X^2 + X^2 = (\sqrt{50})^2$
• Step 2: Simplify the equation:
$2X^2 = 50$
• Step 3: Solve for $X^2$ by dividing each term:
$X^2 = \frac{50}{2} = 25$
• Step 4: Take the square root of both sides to solve for $X$:
$X = \sqrt{25} = 5$

Therefore, the length of $X$ in the right isosceles triangle is $5$.