In a right triangle, one leg has length $6$, the other leg is labeled $x$, and the hypotenuse has length $10$. What is the value of $x$?

• A. $4$
• B. $7$
• C. $12$
• D. $8$

Answer: (D)

Verified step by step guidance

1. Identify the sides of the right triangle: one leg is 6, the other leg is \( x \), and the hypotenuse is 10.
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. Set up the equation using the given values: \( 6^2 + x^2 = 10^2 \).
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 take the square root of both sides to find \( x \).