MATH Middle School
posted by PLEASE HELP on .
The area of two rectangles is 360 square centimeters. The length of the second rectangle is 12 cm greater than the first while its width is 5 cm less than the first. Find the difference of the perimeters of the two rectangles if the lengths and widths are positive integers.

first:
length  x
width y
2nd:
length  x+12
width  y5
xy + (x+12)(y5) = 360
xy + xy + 12y  5x  60 = 360
2xy + 12y  5x = 420
difference in perimeter = 2x + 2y  2(x+12)  2(y5)
= 2x + 2y 2x  24  2y +10
= 14
The fact that their areas total 360 cm^2 appears to not even enter the picture. 
14 cm