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Creating Quadratic Equations

  1. Jan 6, 2012 #1
    Hello PF! I'm having trouble approaching this problem. Any assistance would be greatly appreciated.

    1. The problem statement, all variables and given/known data
    A rectangle with area of 35 cm2 is formed by cutting off strips of equal width from a rectangular piece of paper. The rectangular piece of paper is of 7cm width and 9cm length.

    2. Relevant equations
    ax2+bx+c


    3. The attempt at a solution
    I know that I have to create two separate equations and substitute to solve, however I'm really not certain how to create those equations (more-so what to base them on) . Perhaps a push in the right direction is all I require...
     
  2. jcsd
  3. Jan 6, 2012 #2

    eumyang

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    Homework Helper

    I think you need to clarify what you mean by "cutting off strips of equal width." It sounds ambiguous to me.
     
  4. Jan 6, 2012 #3
    Sorry, I didn't include the actual question. It asks:
    a) what is the width of each strip?
    b) what are the dimensions of the new rectangle?

    In my textbook, the diagram shows a rectangle with sides labeled 9cm and 7cm, and an inner rectangle of area 35 cm squared with unknown dimensions. The strips equal width are labeled as x and are shown to be the distance from one side of the inner rectangle to the closest side of the outer rectangle. I hope that clarifies my question; unfortunately I cannot upload the diagram right now.
     
  5. Jan 6, 2012 #4
    Is this what the diagram looks like
     

    Attached Files:

  6. Jan 6, 2012 #5
    Yes, that's correct.
     
  7. Jan 6, 2012 #6
    Ok think what the lengths of inner rectangle can be expressed as.

    Hint you need to use the length of the corresponding outer side and x.
     
  8. Jan 6, 2012 #7
    Thank you! I think I figured it out:
    A=lw
    35=lw
    35=(7-2x)(9-2x)
    35=63-18x-14x+4x2
    0=4x2-32x+28

    I then factored out the polynomial:
    4x2-4x-28x+28
    4x(x-1)28(x-1)
    (4x-28)(x-1)
    x=1,7

    And since a negative dimension is illogical, 7cm is extraneous and 1 cm is the width of the strip. After that I substituted the value back into the equation, and that yielded 7cm and 5cm as answers.

    Thanks man! You've been a huge help!
     
  9. Jan 6, 2012 #8
    No problem. We did these in school last year and seeing the initial formula to get started is the hardest part. If you keep on trying questions you will eventually get a feel for what types of problem come up regularly and how to deal with them.

    AL
     
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