# MATH Middle School

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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.

• MATH Middle School -

first:
length --- x
width ----y

2nd:
length --- x+12
width --- y-5

xy + (x+12)(y-5) = 360
xy + xy + 12y - 5x - 60 = 360
2xy + 12y - 5x = 420

difference in perimeter = 2x + 2y - 2(x+12) - 2(y-5)
= 2x + 2y -2x - 24 - 2y +10
= -14

The fact that their areas total 360 cm^2 appears to not even enter the picture.

• Frank N. Osborne Middle School -

14 cm

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