A carpet was ordered with its length and width in the ratio 3:2. Later, the dimensions were changed so that the length and width were in the ratio 7:3, while the perimeter remained unchanged. What is the ratio of the areas of the carpet before and after the modification?

Explanation

Let the original length and width be 3x and 2x respectively. For the modified carpet, let the dimensions be 7y and 3y. Since the perimeter remains the same: 2(3x + 2x) = 2(7y + 3y) which simplifies to 5x = 10y, so x = 2y. The ratio of areas is (3x * 2x) : (7y * 3y) = 6x^2 : 21y^2 = 6(2y)^2 : 21y^2 = 6 * 4y^2 : 21y^2 = 24y^2 : 21y^2 = 8 : 7.