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27 February, 08:07

A square and rectangle have equal areas. The length of the rectangle is five inches more than twice the side of the square. The width of the rectangle is 6 inches less than the side of the square. Find the length of the side of the square.

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  1. 27 February, 08:16
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    Just to make things easier, imagine that x is the length of the side of the square:

    According to the information, we can conclude that:

    2x + 5 (inches) is the length of the rectangle.

    x - 6 (inches) is the width of the rectangle.

    Since the areas of the square and the rectangle are the same, we know that:

    (2x + 5) (x - 6) = x²

    2x² - 12x + 5x - 30 = x²

    2x² - 12x + 5x - x² = 30

    x² - 7x - 30 = 0

    x² + 3x - 10x - 30 = 0

    x (x + 3) - 10 (x + 3) = 0

    (x - 10) (x + 3) = 0

    Now we can slove each part independently:

    x - 10 = 0 or x + 3 = 0

    x = 10 or x = - 3

    Since the length of the side of the square can't be a negative number, we can cancel - 3 out and keep 10 only.

    So the length of the side of the square is 10 inches.

    (This is how I usually do to solve problems of this kind)
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