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Area of a Triangle Word Problem

  1. Feb 7, 2012 #1

    S.R

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    1. The problem statement, all variables and given/known data
    If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.


    2. Relevant equations
    N/A

    3. The attempt at a solution
    height = h-5
    base = h

    A=(bh)/2

    52=(h(h-5)/2

    52=(h^2-5h)/2

    104=h^2-5h

    h^2-5h-104=0

    (h-13)(h+8)=0

    h=13 or h=-8

    h=-8 is extraneous; therefore the base is 13 and the height is 8.

    This is Grade 9 review and I don't think my teacher would include a problem using the quadratic equation. Is there an easier solution to this problem?
     
    Last edited: Feb 7, 2012
  2. jcsd
  3. Feb 7, 2012 #2

    eumyang

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    Homework Helper

    There's always guess-and-check, I suppose...

    I'm not sure why you don't think your teacher would include a problem using the quadratic equation. If we assume that Grade 9 = Algebra I (in the US), then sure, solving quadratic equations by factoring is an Algebra I topic.
     
  4. Feb 7, 2012 #3

    S.R

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    In Canada, the Grade 9 curriculum involves linear equations.

    EDIT: I suppose there is guess-and-check. Using a quadratic equation is the only way to algebraically solve the problem.

    /closed
     
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