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16 June, 11:33

Dale has a square garden. He adds a 2-foot-wide walkway around his garden. If the total area of the walkway and garden is 196 square feet, find the dimensions of the garden

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  1. 16 June, 11:58
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    Let the side of the garden alone (without walkway) be x.

    Then the area of the garden alone is x^2.

    The walkway is made up as follows:

    1) four rectangles of width 2 feet and length x, and

    2) four squares, each of area 2^2 square feet.

    The total walkway area is thus x^2 + 4 (2^2) + 4 (x*2).

    We want to find the dimensions of the garden. To do this, we need to find the value of x.

    Let's sum up the garden dimensions and the walkway dimensions:

    x^2 + 4 (2^2) + 4 (x*2) = 196 sq ft

    x^2 + 16 + 8x = 196 sq ft

    x^2 + 8x - 180 = 0

    (x-10 (x+18) = 0

    x=10 or x=-18. We must discard x=-18, since the side length can't be negative. We are left with x = 10 feet.

    The garden dimensions are (10 feet) ^2, or 100 square feet.
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