1. Problem: A rectangular rug has an area of 60 in.² and a perimeter of 34 in. We need to find its dimensions. 2. Let the length be $l$ and the width be $w$. The formulas are: - Area: $A = l \times w = 60$ - Perimeter: $P = 2(l + w) = 34$ 3. From the perimeter formula, solve for $l + w$: $$2(l + w) = 34 \implies l + w = 17$$ 4. Express $l$ in terms of $w$: $$l = 17 - w$$ 5. Substitute into the area formula: $$l \times w = 60 \implies (17 - w)w = 60$$ 6. Expand and rearrange: $$17w - w^2 = 60 \implies w^2 - 17w + 60 = 0$$ 7. Factor the quadratic: $$w^2 - 17w + 60 = (w - 12)(w - 5) = 0$$ 8. So, $w = 12$ or $w = 5$. Corresponding $l$ values: - If $w = 12$, then $l = 17 - 12 = 5$ - If $w = 5$, then $l = 17 - 5 = 12$ 9. Dimensions are $5$ in by $12$ in. Final answer: The dimensions are 5 and 12 inches.