A right triangle has legs of lengths $6$ and $8$. What is the length of the hypotenuse?

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

Answer: (C)

Verified step by step guidance

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