Given a right triangle where the length of one leg is $x_s=10$ and the length of the other leg is $x_y=24$, what is the length of the hypotenuse $r_y$?

• A. $26$
• B. $20$
• C. $14$
• D. $34$

Answer: (A)

Verified step by step guidance

1. Identify the given sides of the right triangle: one leg is \(x_{s} = 10\) and the other leg is \(x_{y} = 24\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse \(r_{y}\) is equal to the sum of the squares of the legs: \(r_{y}^2 = x_{s}^2 + x_{y}^2\).
3. Substitute the known values into the Pythagorean theorem: \(r_{y}^2 = 10^2 + 24^2\).
4. Calculate the squares of the legs (but do not find the final sum): \$10^2 = 100\( and \)24^2 = 576$.
5. Add these squared values to express \(r_{y}^2\) as \(r_{y}^2 = 100 + 576\), then take the square root of both sides to find \(r_{y} = \sqrt{100 + 576}\).