A right triangle has legs measuring $26$ ft and $34$ ft. What is the length of the hypotenuse of the triangle?

• A. $74$ ft
• B. $58$ ft
• C. $68$ ft
• D. $60$ ft

Answer: (A)

Verified step by step guidance

1. Identify the given sides of the right triangle: the legs are 26 ft and 34 ft.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (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: \(c^2 = 26^2 + 34^2\).
4. Calculate the squares of the legs: \$26^2 = 676\( and \)34^2 = 1156$.
5. Add these values to find \(c^2\): \(c^2 = 676 + 1156\), then take the square root of the sum to find the length of the hypotenuse \(c = \sqrt{676 + 1156}\).