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Math Help - Partition a Square

  1. #1
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    Partition a Square

    A square measuring 10 centimeter on a side is divided by vertical and horizontal line segment into rectangles with area of 12, 18, 28, and 42 square centimeters. Where should the vertical and horizontal lines be located? Draw a diagram.
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  2. #2
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    Hello, aznmartinjai!

    A square measuring 10 centimeter on a side
    is divided by a vertical and a horizontal line segment
    into rectangles with area of 12, 18, 28, and 42 cm.
    Where should the vertical and horizontal lines be located? .Draw a diagram.
    Code:
              x       10-x
          * - - - * - - - - - *
          |       |           |
        y |   12  |     18    | y
          |       |           |
          * - - - + - - - - - *
          |       |           |
          |       |           |
     10-y |   28  |     42    |
          |       |           |
          |       |           |
          * - - - * - - - - - *

    In the upper-left, we have a rectangle: .xy .= .12 . [1]

    In the upper-right, another rectangle: .y(10 - x) .= .18 .[2]

    From [2], we have: .10y - xy .= .18
    . . . . . . . . . . . . . . . . . . .
    Substitute [1]: . . . 10y - 12 .= .18 . . 10y = 30 . . y = 3

    Substitute into [1]: .x3 = 12 . . x = 4


    The solution looks like this:
    Code:
              4         6
          * - - - * - - - - - *
          |       |           |
        3 |   12  |     18    |
          |       |           |
          * - - - + - - - - - *
          |       |           |
          |       |           |
        7 |   28  |     42    |
          |       |           |
          |       |           |
          * - - - * - - - - - *
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