Given a right triangle where one leg has length $6$, the other leg has length $8$, and the hypotenuse is $x$, what is the value of $x$?

• A. $14$
• B. $12$
• C. $8$
• D. $10$

Answer: (D)

Verified step by step guidance

1. Identify the sides of the right triangle: the two legs are given as 6 and 8, and the hypotenuse is labeled as \( x \).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs: \( x^2 = a^2 + b^2 \).
3. Substitute the known leg lengths into the Pythagorean theorem: \( x^2 = 6^2 + 8^2 \).
4. Calculate the squares of the legs: \( 6^2 = 36 \) and \( 8^2 = 64 \), then add them together: \( 36 + 64 \).
5. Take the square root of the sum to solve for \( x \): \( x = \sqrt{36 + 64} \).