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13 July, 19:40

22) 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. 13 July, 20:08
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    Here two areas are equal: That of the square equals that of the rectangle.

    Let s represent the side length of the square. Then the area of the square is s^2.

    The length of the rect. is 2s+5, and the width of the rect. is s-6.

    " A square and rectangle have equal areas."

    Thus, s^2 = (2s+5) (s-6), or s^2 = 2s^2 - 12s + 5s - 30

    Simplifying, 0 = s^2 - 7s - 30. This factors to 0 = (s-10) (s+3).

    Thus, s may be either 10 or - 3. Lengths are not negative, so omit the - 3. The side of the square, s, is 10 units.

    Then the width of the rect. is s-6 = 4, and the length of the rect. is 2s+5, or 2 (10) + 5, or 25.
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