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26 October, 09:27

The area of a rectangle is 35 feet^2, and the length of the rectangle is 8 feet less than three times the width. Find the dimensions of the rectangle

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  1. 26 October, 13:04
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    A = 35 ft^2 (square feet)

    L=3W-8 (feet)

    The formula for the area of this rect. is now A = W (3W-8) = 35 ft^2

    3W^2 - 8W - 35 = 0

    There are various ways in which we could solve this equation for W.

    I have chosen to "factor by grouping."

    3W^2 - 8W - 35 = 0

    3W^2 - 15W + 7W - 35 = 0

    3W (W-5) + 7 (W-5) = 0

    Then (3W+7) (W-5) = 0, and W=-7/3 or W=5. Since W denotes width, and width cannot be negative, omit W=-7/3. Thus, W=width=5 feet.

    Next, L=3W-8=3 (5) - 8=15-8=7 feet.

    Check: Does (5 feet) (7 feet) come out to 35 square feet? YES.

    The dimensions of this rectangle are 5 by 7 feet.
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