A right triangle has one leg of length $9$ meters and the other leg of length $9$ meters. What is the length of the hypotenuse in meters?

• A. $9$
• B. $9\surd 2$
• C. $12$
• D. $18$

Answer: (B)

Verified step by step guidance

1. Identify the type of triangle given: it is a right triangle with two legs of equal length, each measuring 9 meters.
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 known leg lengths into the Pythagorean theorem: \(c^2 = 9^2 + 9^2\).
4. Simplify the expression by calculating the squares: \(c^2 = 81 + 81\).
5. Add the values and then take the square root of both sides to solve for \(c\): \(c = \sqrt{162}\), which can be simplified further.