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Math Help - Completing the Square Word Problem

  1. #1
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    Completing the Square Word Problem

    Alright I'm not exactly sure what category this question falls under, but it was a question part of a "completing the square" unit.

    A rectangle is 6m longer than wide. The diagonal is 30m. Find the dimensions of the rectangle.

    I drew a diagram, L representing Length and W representing Width.

    (w)^2+(w+6)^2=(30)^2
    w^2+w^2+36=900
    w^2+w^2=900-36
    2w^2=864
    w^2=432
    w=sqrt 432
    w=20.8m

    Then I subbed w=20.8m into L = W +6 to find L.

    L = 26.8M

    So the dimensions were 20.8m and 26.8m. For some reason this doesn't look right. No completing the square was involved in this question. Is my answer correct?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shadow6 View Post
    Alright I'm not exactly sure what category this question falls under, but it was a question part of a "completing the square" unit.

    A rectangle is 6m longer than wide. The diagonal is 30m. Find the dimensions of the rectangle.

    I drew a diagram, L representing Length and W representing Width.

    (w)^2+(w+6)^2=(30)^2
    w^2+w^2+36=900
    w^2+w^2=900-36
    2w^2=864
    w^2=432
    w=sqrt 432
    w=20.8m

    Then I subbed w=20.8m into L = W +6 to find L.

    L = 26.8M

    So the dimensions were 20.8m and 26.8m. For some reason this doesn't look right. No completing the square was involved in this question. Is my answer correct?
    common mistake: thinking that (a + b)^2 = a^2 + b^2. this is wrong!

    rather, (a + b)^2 = a^2 + 2ab + b^2

    hence (w + 6)^2 = w^2 + 12w + 36

    now fix your problem
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  3. #3
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    Forgot about that, thanks for the info.
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  4. #4
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    You should learn to type in LaTex. It really makes reading much easier.

    \begin{aligned}<br />
w^2 + (w + 6)^2 &= 30^2 \\<br />
w^2 + w^2 + 12w  + 36 &= 900 \\<br />
2w^2 + 12w  + 36 &= 900 \\<br />
 2w^2 + 12w  &= 864 \\<br />
  w^2 + 6w  &= 432 \\<br />
   \end{aligned}
    ^ Here is where you should complete the square. I'll leave the rest up to you.


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  5. #5
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    Dimensions are 18m by 24m.

    Only 3 more questions left out of my 122 question project.
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