1. **Problem Statement:** Determine whether each statement about the right triangular prism with base edges 3 m, 4 m, hypotenuse 5 m, and height $x$ m is true or false given the surface area is 72 m². 2. **Formula for Surface Area of a Right Triangular Prism:** The surface area $S$ is given by: $$S = ext{Perimeter of triangular base} \times \text{height} + 2 \times \text{Area of triangular base}$$ 3. **Calculate the perimeter of the triangular base:** $$P = 3 + 4 + 5 = 12$$ 4. **Calculate the area of the triangular base:** Since it is a right triangle with legs 3 m and 4 m, $$\text{Area} = \frac{1}{2} \times 3 \times 4 = 6$$ 5. **Write the surface area equation with known values:** $$72 = 12x + 2 \times 6$$ 6. **Simplify the equation:** $$72 = 12x + 12$$ 7. **Isolate $x$:** $$72 - 12 = 12x$$ $$60 = 12x$$ 8. **Divide both sides by 12:** $$\cancel{12}x = \frac{60}{\cancel{12}}$$ $$x = 5$$ 9. **Conclusion:** The height $x$ of the prism is 5 m. Any statement about the prism's height or surface area can be checked using this value.