Solution: Let the short side length of a rectangle with an aspect ratio of 2: 1 be x, then the long side length is 2x and the area is 2x^2；; Circumference 6x;

The circumference of a rectangle with an aspect ratio of 3: 2 is -6x,

The long side length is 3(a-6x)/5, and the short side length is 2(a-6x)/5.

The area is [6 (a-6x) 2]/25.

Let the sum of areas be y, then

y=2x^2+[6(a-6x)^2]/25

=[50x^2+6(a^2- 12ax+36x^2)]/25

=(266x^2-72ax+6a^2)/25

You can get guidance from both sides and do it yourself.