In a right triangle, one leg has length $6$ and the other leg has length $8$. What is the length of the hypotenuse $x$? Select the correct answer.

• A. $12$
• B. $14$
• C. $9$
• D. $10$

Answer: (D)

Verified step by step guidance

1. Identify the given information: the two legs of the right triangle have lengths 6 and 8.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse \(x\) is equal to the sum of the squares of the legs: \(x^2 = a^2 + b^2\).
3. Substitute the given leg lengths into the formula: \(x^2 = 6^2 + 8^2\).
4. Calculate the squares of the legs: \$6^2 = 36\( and \)8^2 = 64\(, so \)x^2 = 36 + 64$.
5. Add the values and then take the square root of both sides to solve for \(x\): \(x = \sqrt{36 + 64}\).