the area of a rectangular wall of a barn is 252 square ft. its length is 10 ft longer than twice its width. find the lenght and width of th

Question

the area of a rectangular wall of a barn is 252 square ft. its length is 10 ft longer than twice its width. find the lenght and width of the barn​

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Gianna 2 weeks 2021-10-11T00:15:09+00:00 1 Answer 0

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    0
    2021-10-11T00:16:45+00:00

    Answer:

    L=9 ft

    W=28 ft

    Step-by-step explanation:

    LW=252

    L=10+2W

    Plug 2nd into 1st

    (10+2W)W=252

    Distribute

    10W+2W^2=252

    Divide both sides by 2

    5W + W^2=126

    Reorder using commutative property

    W^2+5W =126

    Subtract 126 on both sides

    W^2+5W-126=0

    What are two numbers multiply to be -126 and add to be 5?

    My scratch paper:

    -126=-2(63)

    -126=-2(7)(9)

    -126=-14(9)

    So 14(-9) is -126 and 14+(-9)=5 so these are our magic numbers

    (W+14)(W-9)=0

    W=-14 or W=9

    So W=9 is what makes sense here sense length can’t be negative

    Now let’s go back and find L…

    L=10+2W=10+2(9)=10+18=28

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