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 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets? Pick:
A) 4 : 5
B) 9 : 10
C) 14 : 15
D) 19 : 20
E) 24 : 25

Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 ( 3 x + 2 x ) = 2 ( y + y ) 5 x = 2 y ( 5 / 2 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : ( 25 / 4 ) * x ^ 2 = 24 : 25 the answer is e ."
Answer: E