1. **State the problem:** We are given the areas of the faces of a rectangular prism's net and need to find its dimensions (length, width, height) in inches. 2. **Given areas:** The net shows rectangles with areas 30 in², 50 in², and 60 in². 3. **Recall:** The faces of a rectangular prism are rectangles with areas equal to the product of two dimensions. Let the dimensions be $x$, $y$, and $z$. 4. **Assign areas to faces:** The prism has three pairs of opposite faces with areas: - $xy = 30$ - $yz = 50$ - $xz = 60$ 5. **Use these equations:** $$xy = 30$$ $$yz = 50$$ $$xz = 60$$ 6. **Find dimensions:** Multiply all three equations: $$ (xy)(yz)(xz) = 30 \times 50 \times 60 $$ $$ (xyz)^2 = 90000 $$ $$ xyz = \sqrt{90000} = 300 $$ 7. **Solve for each dimension:** $$ x = \frac{xyz}{yz} = \frac{300}{50} = 6 $$ $$ y = \frac{xyz}{xz} = \frac{300}{60} = 5 $$ $$ z = \frac{xyz}{xy} = \frac{300}{30} = 10 $$ 8. **Check:** $$ xy = 6 \times 5 = 30 $$ $$ yz = 5 \times 10 = 50 $$ $$ xz = 6 \times 10 = 60 $$ All match the given areas. **Final answer:** The dimensions are $6$, $5$, and $10$ inches.