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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