1. **State the problem:** We are given a right rectangular prism with dimensions 8 cm, 5 cm, and $x$ cm. The total surface area is 236 cm². We need to find the value of $x$. 2. **Formula for surface area of a rectangular prism:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height. 3. **Assign dimensions:** Let $l = 8$, $w = 5$, and $h = x$. 4. **Write the surface area equation:** $$236 = 2(8 \times 5 + 8 \times x + 5 \times x)$$ 5. **Simplify inside the parentheses:** $$236 = 2(40 + 8x + 5x)$$ $$236 = 2(40 + 13x)$$ 6. **Distribute the 2:** $$236 = 80 + 26x$$ 7. **Isolate $x$:** $$236 - 80 = 26x$$ $$156 = 26x$$ 8. **Divide both sides by 26:** $$\frac{156}{\cancel{26}} = \frac{26x}{\cancel{26}}$$ $$6 = x$$ **Final answer:** $$x = 6$$ cm