1. **State the problem:** We have a right triangle with one leg of length 7.5 yd, hypotenuse 9.3 yd, and the other leg labeled $a$. We need to find the perimeter, which is the sum of all sides. 2. **Use the Pythagorean theorem:** For a right triangle, the relationship between the legs and hypotenuse is $$a^2 + b^2 = c^2$$ where $a$ and $b$ are legs and $c$ is the hypotenuse. 3. **Plug in known values:** Here, $b = 7.5$ yd and $c = 9.3$ yd, so $$a^2 + 7.5^2 = 9.3^2$$ 4. **Calculate squares:** $$a^2 + 56.25 = 86.49$$ 5. **Isolate $a^2$:** $$a^2 = 86.49 - 56.25$$ 6. **Simplify:** $$a^2 = 30.24$$ 7. **Find $a$ by taking the square root:** $$a = \sqrt{30.24} = 5.5$$ yd (rounded to nearest tenth) 8. **Calculate perimeter:** $$P = a + b + c = 5.5 + 7.5 + 9.3 = 22.3$$ yd **Final answer:** The perimeter is **22.3 yards**.