1. **State the problem:** We have a rectangle with side lengths 5 and 10 units. It is dilated by a scale factor of 5. We need to find the perimeter and area of the original rectangle and the dilated rectangle. 2. **Formulas:** - Perimeter of a rectangle: $$P = 2(l + w)$$ where $l$ is length and $w$ is width. - Area of a rectangle: $$A = l \times w$$ - When a figure is dilated by a scale factor $k$, all lengths are multiplied by $k$. - Perimeter scales by $k$. - Area scales by $k^2$. 3. **Calculate perimeter of original rectangle:** $$P = 2(5 + 10) = 2(15) = 30$$ units 4. **Calculate area of original rectangle:** $$A = 5 \times 10 = 50$$ units² 5. **Calculate side lengths of dilated rectangle:** $$l' = 5 \times 5 = 25$$ units $$w' = 10 \times 5 = 50$$ units 6. **Calculate perimeter of dilated rectangle:** $$P' = 2(25 + 50) = 2(75) = 150$$ units 7. **Calculate area of dilated rectangle:** $$A' = 25 \times 50 = 1250$$ units² **Final answers:** - Perimeter of original rectangle: 30 units - Area of original rectangle: 50 units² - Perimeter of dilated rectangle: 150 units - Area of dilated rectangle: 1250 units²