Answer: Let a rectangle be 3 times longer and 2 times wider.

Let the length of rectangle B be 7y and the width be 5y.

So 2*(3x+2x)=2*(7y+5y)

So 10x=24y.

So x:y= 12:5.

Because the area of a rectangle is 6x square, and the area of b rectangle is 35y square.

So the area ratio of A and B is 864:875.

Method 2

The length and width of rectangle A are divided into 5 parts, and the length and width of rectangle B are divided into 12 parts. The least common multiple of 5 and 12 is 60 parts.

The length and width of a rectangle are 3:2=36:24.

B The length and width of the rectangle are 7:5=35:25.

Because the area of a rectangle is equal to length x width,

So the area of rectangle A: the area of rectangle B =(36×24):(35×25)=864:875.