1. **Problem statement:** The length of a rectangle is 7 cm longer than its width. The perimeter of the rectangle is 74 cm. We need to find the length and the area of the rectangle. 2. **Formula used:** The perimeter $P$ of a rectangle is given by $$P = 2(\text{length} + \text{width})$$ 3. **Define variables:** Let the width be $w$ cm. Then the length is $w + 7$ cm. 4. **Set up the equation:** Using the perimeter formula, $$74 = 2((w + 7) + w)$$ 5. **Simplify the equation:** $$74 = 2(2w + 7)$$ $$74 = 4w + 14$$ 6. **Solve for $w$:** $$4w = 74 - 14$$ $$4w = 60$$ $$w = \frac{60}{4} = 15$$ cm 7. **Find the length:** $$\text{length} = w + 7 = 15 + 7 = 22$$ cm 8. **Calculate the area:** The area $A$ of a rectangle is $$A = \text{length} \times \text{width} = 22 \times 15 = 330$$ cm$^2$ **Final answer:** The length is 22 cm and the area is 330 cm$^2$.