1. **State the problem:** We have a triangular prism with a triangular base where one side is 15 cm and the height of the triangle is 8 cm. The volume of the prism is given as 720 cm³. We need to find the height $x$ of the prism. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Height of prism}$$ 3. **Calculate the base area:** The base is a triangle with base 15 cm and height 8 cm, so $$\text{Base Area} = \frac{1}{2} \times 15 \times 8 = \frac{1}{2} \times 120 = 60 \text{ cm}^2$$ 4. **Use the volume formula:** $$720 = 60 \times x$$ 5. **Solve for $x$:** $$x = \frac{720}{60}$$ 6. **Simplify the fraction:** $$x = \frac{\cancel{720}^{12}}{\cancel{60}^{1}} = 12$$ 7. **Answer:** The height of the prism is $12$ cm.