An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 3 but were was no change in its perimeter. What is the ratio of the areas of the carpets?  Choose the correct choice from the following answers
A) 9:10
B) 19:20
C) 29:30
D) 39:40
E) 49:50
Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be 4y and 3y.   2(3x + 2x) = 2(4y + 3y)   5x = 7y   (5/7) * x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : 4y * 3y   = 6x^2 : 12y^2   = x^2 : 2y^2   = x^2 : 2*(25/49) * x^2   = 49 : 50   The answer is 49:50.
<result>E</result>
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 3 but were was no change in its perimeter. What is the ratio of the areas of the carpets?