Joe has a rectangular chicken coop. The length of the coop is 4 feet less than twice the width. The area of the chicken coop is 510 square f

Question

Joe has a rectangular chicken coop. The length of the coop is 4 feet less than twice the width. The area of the chicken coop is 510 square feet. What is the length of the chicken coup?

PLEASE HELP ME!!!

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Adeline 1 week 2021-11-25T10:44:01+00:00 1 Answer 0

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    2021-11-25T10:45:04+00:00

    Let w and l be the dimensions (width and length, respectively) of the coop.

    We know that the length of the coop is 4 feet less than twice the width, which means that

    l=2w-4

    Also, the area is 510, but the area is the product of the dimensions, so we have

    lw=510

    Plug the expression for l in the formula for the area:

    lw=(2w-4)w=510 \iff 2w^2-4w-510=0

    We can divide the whole expression by 2 and solve it with the quadratic formula:

    w^2-2w-255=0 \iff w=\dfrac{2\pm\sqrt{4+1020}}{2}=\dfrac{2\pm 32}{2}=1\pm 16

    So, the two solutions are

    w_1=1-16=-15,\quad w_2=1+16=17

    The negative solution makes no sense (we can’t have negative lengths), so the width must be 17.

    We conclude that the length is

    l=2w-4=2\cdot 17-4=34-4=30

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