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What fraction has the length of the rectangle been reduced?

  1. Jul 17, 2017 at 6:53 AM #1
    1. The problem statement, all variables and given/known data
    The width of a rectangle is increased by one tenth, but the area remains the same. By what fraction has the length of the rectangle been reduced?

    3. The attempt at a solution
    Length = x
    Width = x + 1/10

    Set equation:
    L * W
    x *(10x + x)
    10x^2 + x^2

    I am stuck... Please help...
     
  2. jcsd
  3. Jul 17, 2017 at 7:15 AM #2
    Why do you assume the length and width are initially equal? What is the width after increasing (It is not x + 1/10).
    Try writing Before: length = L, width = W. After: length = Lx, width = Wy where x and y are constants. What is y? Therefore what is x?
     
  4. Jul 17, 2017 at 7:17 AM #3
    Length = L*x
    Width = W*y
    where x and y are constants

    W*(1/10) and L*x
     
  5. Jul 17, 2017 at 7:44 AM #4

    scottdave

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    When i read this:
    I interpret as "the width is increased by 1/10 (of the original width)" or New_Width = Old_Width + Old_Width*(1/10)
    I believe this is how the problem intends. Keep the area constant (set the new area equal to original).
     
  6. Jul 17, 2017 at 7:54 AM #5
    original dimensions ---- w by l
    original area = wl

    new width = 9w/10
    new length = L
    L(9w/10) = lw
    L = lw/(9w/10) = (10/9)l = 1.111..
    so the length would have to increase which does not make sense as it says reduce in question.
    The increase is 10/9 of the original or appr 11.1%
     
  7. Jul 17, 2017 at 7:57 AM #6

    scottdave

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    It looks like you are on the right track with the formulas, but you have the new width less than the original, while the problem states that it was increased.
     
  8. Jul 17, 2017 at 8:01 AM #7
    new width = w + w/10
    new length = L
    L(11w/10) = lw
    L = lw/(11w/10) = (10/11)l = 0.90909....
    so the length would have to increase by 10/11 of the original or appr 9.09%

    Is this correct please?
     
  9. Jul 17, 2017 at 8:04 AM #8

    scottdave

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    Your numerical answer is correct, but the conclusion is not.
    Since area is constant, if one dimension increases what happens to the other one? Think in extremes. If one dimension doubles, what happens to the other one?
     
  10. Jul 17, 2017 at 8:06 AM #9
    so the length would have to decrease by 10/11 of the original or appr 9.09%
     
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