Math

A large rectangle is divided into 4 non-overlapping smaller rectangles by two lines. One line is parallel to the base, and the other line is parallel to the height. If the areas of three of the small rectangles are 18,24, and 40, compute the only possible integer solution for the area of the fourth small rectangle. I'm not entirely sure where to start.

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asked by Joe
  1. The original rectangle and the four smaller rectangles are related by the sides: side 1=a+b and side 2=c+d such that the areas of the small rectangles are:
    ac, ad, bc, bd.

    By factoring each area, and look for possible candidates for a,b,c and d to satisfy the above relations, we can find the sides of the fourth rectangle.

    The first part is done for you below:

    18=(2*3)*(3*3)
    24=(2*2)*(2*3)
    40=(2*2)*(2*5)
    The fourth rectangle=?

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  2. 18=(2*3)*(3*3)???

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  3. 18=(2*3)*(3*3)???

    This doesn't work

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    posted by joe

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