In a right triangle, one leg has length $6$ and the hypotenuse has length $10$. If $x$ is the length of the other leg, select the correct value of $x$.

• A. $\sqrt{36}$
• B. $\sqrt{16}$
• C. $\sqrt{64}$
• D. $\sqrt{100}$

Answer: (C)

Verified step by step guidance

1. Identify the given elements in the right triangle: one leg has length 6, the hypotenuse has length 10, and the other leg length is denoted as \( x \).
2. 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: \( a^2 + b^2 = c^2 \).
3. Assign the known values to the formula: \( 6^2 + x^2 = 10^2 \).
4. Calculate the squares of the known sides: \( 36 + x^2 = 100 \).
5. Isolate \( x^2 \) by subtracting 36 from both sides: \( x^2 = 100 - 36 \), then find \( x \) by taking the square root of both sides: \( x = \sqrt{100 - 36} \).