Amanda needs to make a garden plot which has an area less than 18 sq. feet. The length should be 3 feet longer than the width. What are the

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Amanda needs to make a garden plot which has an area less than 18 sq. feet. The length should be 3 feet longer than the width. What are the possible dimensions of the garden plot?

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Kim Cúc 5 years 2021-07-28T18:50:20+00:00 1 Answers 25 views 0

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  1. huyenthanh
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    2021-07-28T18:51:46+00:00
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    Answer:

    Any width less than 3 feet

    Step-by-step explanation:

    Inequalities

    The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:

    A = L.W

    The first condition can be written as follows:

    LW < 18

    The length should be 3 feet longer than the width, thus:

    L = W + 3

    Substituting in the inequality:

    (W + 3)W < 18

    Operating and rearranging:

    W^2 + 3W - 18 < 0

    Factoring:

    (W-3)(W+6)<0

    Since W must be positive, the only restriction comes from:

    W – 3 < 0

    Or, equivalently:

    W < 3

    Since:

    L = W + 3

    W = L – 3

    This means:

    L – 3 < 3

    L < 6

    The width should be less than 3 feet and therefore the length will be less than 6 feet.

    If the measures are whole numbers, the possible dimensions of the garden plot are:

    W = 1 ft, L = 4 ft

    W = 2 ft, L = 5 ft

    Another solution would be (for non-integer numbers):

    W = 2.5 ft, L = 5.5 ft

    There are infinitely many possible combinations for W and L as real numbers.

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