In a right triangle with legs of length $14$ and $48$, what is the length of the hypotenuse?

• A. $50$
• B. $49$
• C. $62$
• D. $52$

Answer: (A)

Verified step by step guidance

1. Identify the given information: the triangle is right-angled with legs of lengths 14 and 48.
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: \(c^2 = 14^2 + 48^2\).
4. Calculate the squares of the legs separately: \$14^2 = 196\( and \)48^2 = 2304$.
5. Add these values to find \(c^2\): \(c^2 = 196 + 2304\), then take the square root of the sum to find \(c\): \(c = \sqrt{196 + 2304}\).