1. **State the problem:** We have a right triangle with one leg of length 9 yards, a hypotenuse of length 15 yards, and the other leg labeled as $b$. We need to find the perimeter of the triangle, which is the sum of all its sides. 2. **Use the Pythagorean theorem:** For a right triangle, the relationship between the legs and the hypotenuse is given by: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Plug in the known values:** Here, $a = 9$, $c = 15$, and $b$ is unknown. $$9^2 + b^2 = 15^2$$ 4. **Calculate squares:** $$81 + b^2 = 225$$ 5. **Isolate $b^2$:** $$b^2 = 225 - 81$$ $$b^2 = 144$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{144} = 12$$ 7. **Calculate the perimeter:** $$P = a + b + c = 9 + 12 + 15 = 36$$ **Final answer:** The perimeter of the triangle is **36 yards**.