Given a right triangle where one leg has length $5$ units and the other leg has length $12$ units, what is the length of the hypotenuse? Round your answer to the nearest hundredth.

• A. $17.00$
• B. $7.00$
• C. $13.00$
• D. $12.50$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the two legs of the right triangle have lengths 5 units and 12 units.
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: \(c^2 = 5^2 + 12^2\).
4. Calculate the squares of the legs: \$5^2 = 25\( and \)12^2 = 144\(, then add them to get \)c^2 = 25 + 144$.
5. Take the square root of both sides to solve for \(c\): \(c = \sqrt{25 + 144}\), which gives the length of the hypotenuse.