The problem asks us to find the length of the hypotenuse of a right triangle with legs of length 9 and 12. The length of the hypotenuse is denoted by $c$.

1. Problem Description

The problem asks us to find the length of the hypotenuse of a right triangle with legs of length 9 and

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2. The length of the hypotenuse is denoted by $c$.

2. Solution Steps

We can use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs). Let $a$ and $b$ be the lengths of the legs, and $c$ be the length of the hypotenuse. Then,

$a^2 + b^2 = c^2$

In this problem, $a = 9$ and $b = 12$. Plugging these values into the Pythagorean theorem gives:

$9^2 + 12^2 = c^2$

$81 + 144 = c^2$

$225 = c^2$

To find $c$, we take the square root of both sides:

$c = \sqrt{225}$

$c = 15$

3. Final Answer

$c = 15$