calculate hypotenuse of right triangle with legs 9 and 12

1. Identify the given information: We are given a right triangle with two legs measuring $a = 9$ feet and $b = 12$ feet. We need to find the length of the hypotenuse, denoted as $c$.

1. Apply the Pythagorean theorem: The Pythagorean theorem states that for any right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is $a^2 + b^2 = c^2$.

3. Substitute the values into the formula: Plug in the given values for the legs:
$$9^2 + 12^2 = c^2$$

4. Calculate the squares: Calculate the squares of the legs:
$$81 + 144 = c^2$$

5. Sum the values: Add the results together:
$$225 = c^2$$

6. Solve for c: Take the square root of both sides to find the length of the hypotenuse:
$$c = \sqrt{225}$$
$$c = 15$$

The length of the hypotenuse is 15 feet, which corresponds to option D.