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Math Help - Rectangle?

  1. #1
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    Rectangle?

    Hi!
    There's again something too difficult for me, I hope you can help me
    You have a garden whose area is 18 sq ft and perimeter's 18 ft. It's length is x and width is y.

    The first question says to write equations about this, and I think I've gone so far: a=x*y. p=2y+2x. Right? OK. Now comes the extremly difficult part:


    1)Prove that (x+y)^2-4xy=(x-y)^2?
    With the expand-and-solve thing I ended up with this: x^2+y^2-4xy=x^2+y^2. Is that right? And how can it help me prove that (x+y)^2-4xy=(x-y)^2?

    2)Using the results of question 1, calculate (x-y)^2 and find x-y.

    3)Using the results of question 2, calculate x and y.
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  2. #2
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    Quote Originally Posted by Catherine View Post
    Hi!
    There's again something too difficult for me, I hope you can help me
    You have a garden whose area is 18 sq ft and perimeter's 18 ft. It's length is x and width is y.

    The first question says to write equations about this, and I think I've gone so far: a=x*y. p=2y+2x. Right? OK. Now comes the extremly difficult part:


    1)Prove that (x+y)^2-4xy=(x-y)^2?
    With the expand-and-solve thing I ended up with this: x^2+y^2-4xy=x^2+y^2. Is that right? And how can it help me prove that (x+y)^2-4xy=(x-y)^2?

    2)Using the results of question 1, calculate (x-y)^2 and find x-y.

    3)Using the results of question 2, calculate x and y.
    (x+y)^2-4xy expand the binomial and we get

    x^2+2xy+y^2-4xy=x^2-2xy-y^2 now we factor

    x^2-2xy+y^2=(x-y)(x-y)=(x-y)^2

    I hope this get started.

    Good luck
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    (x+y)^2-4xy expand the binomial and we get

    x^2+2xy+y^2-4xy=x^2-2xy-y^2 now we factor

    x^2-2xy+y^2=(x-y)(x-y)=(x-y)^2

    I hope this get started.

    Good luck
    Thanks So for question n 2 this means that (x-y)^2=x^2+y^2-2xy. But how can this help me find x-y and how can I calculate x and y using this? Thanks.
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  4. #4
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    You know that 18 = 2x+2y which gives you (x+y) = 9. also xy = 18.

    So (x-y)^2 = (x+y)^2 -4xy = 9^2 - 4*8 = 81-72 = 9

    So (x-y) = 3

    Solve for x and y.
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  5. #5
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    Thanks! Now this is resolved!
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