1. **State the problem:** We have two rectangles A and B. Rectangle A has dimensions $4x$ cm and $2.5$ cm. Rectangle B has dimensions $(2x - 3)$ cm and $7$ cm. The areas of rectangles A and B are equal. We need to find the perimeter of rectangle B. 2. **Write the formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 3. **Set up the equation for equal areas:** $$4x \times 2.5 = (2x - 3) \times 7$$ 4. **Simplify both sides:** $$10x = 7(2x - 3)$$ 5. **Expand the right side:** $$10x = 14x - 21$$ 6. **Bring all terms to one side:** $$10x - 14x = -21$$ $$\cancel{10x} - 14x = -21$$ $$-4x = -21$$ 7. **Divide both sides by -4:** $$x = \frac{-21}{-4} = \frac{21}{4} = 5.25$$ 8. **Find the dimensions of rectangle B:** Width: $2x - 3 = 2(5.25) - 3 = 10.5 - 3 = 7.5$ cm Height: $7$ cm (given) 9. **Calculate the perimeter of rectangle B:** Formula for perimeter of rectangle: $$P = 2(\text{length} + \text{width})$$ $$P = 2(7.5 + 7) = 2(14.5) = 29$$ cm **Final answer:** The perimeter of rectangle B is $29$ cm.