What is the length of the hypotenuse of a right triangle with legs measuring $7$ inches and $8$ inches?

• A. $\sqrt{49}$ inches
• B. $15$ inches
• C. $\sqrt{113}$ inches
• D. $\sqrt{56}$ inches

Answer: (C)

Verified step by step guidance

1. Identify the given information: the legs of the right triangle measure 7 inches and 8 inches.
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 \(a\) and \(b\): \(c^2 = a^2 + b^2\).
3. Substitute the given leg lengths into the formula: \(c^2 = 7^2 + 8^2\).
4. Calculate the squares of the legs: \$7^2 = 49\( and \)8^2 = 64\(, so \)c^2 = 49 + 64$.
5. Add the values to find \(c^2\): \(c^2 = 113\), then take the square root of both sides to find the hypotenuse length: \(c = \sqrt{113}\) inches.