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Isosceles Triangle Geometry Problem

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data
    The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible.

    2. Relevant equations



    3. The attempt at a solution
    Well, I set up three different triangles, to account for the different placements of the sides; but I only came up with one solution. Where is the second solution coming from?
     
  2. jcsd
  3. Feb 21, 2012 #2

    Dick

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    Two of those sides must be equal, right? Pick two of them, set them equal and find x. There are actually three different ways to do that. You'll find one value of x doesn't work.
     
  4. Feb 21, 2012 #3
    Well, I did do that, and I got -8, -6, and 2.
     
  5. Feb 21, 2012 #4

    Dick

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    Are those the x values? How did you get -8 and -6? I did get x=2 for one pair.
     
  6. Feb 22, 2012 #5
    Oh! terribly sorry: I meant to write -4 and -3. And I found them by creating three different triangles, each case having its side equal to on of the others. For instance, I said a = x + 5,
    b = 3x + 13, and c = 4x + 11; then I arbitrarily assigned a and b to be the equivalent sides and set them equal to each other and solved for x. Then, in the second case, I said a = x + 5, but this time I set b = 4x + 11; and once again, I said that a and b were the sides of the isosceles triangle that were equal and consequently set them equal to each other and solved for x. I followed the same procedure for the third case.
     
  7. Feb 22, 2012 #6

    Dick

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    And which one of those gave you x=(-3)? I'm ok with x=2 and x=(-4).
     
  8. Feb 22, 2012 #7
    Blimey, I erred once again; the -3 should be a -2, and I found it by setting x + 5 = 4x + 11
     
  9. Feb 22, 2012 #8

    Dick

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    Ok, so you've got x=2, -2 or -4. Which of those correspond to real triangles? Check what the side lengths are in each case.
     
  10. Feb 22, 2012 #9
    Oh, okay, I see: I never plugged the values back into each expression; as soon as I saw the negative value, I completely dismissed it, thinking that you can't have a negative measurement. So, the two answers should be 2 and -2? and this corresponds to two possible triangles?
     
  11. Feb 22, 2012 #10

    Dick

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    Yes, x=(-4) gives you a side with negative length. Can't have that.
     
  12. Feb 22, 2012 #11
    Okay, thank you so very much for your time and help.
     
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