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A simple problem that's dirving me crazy (Perimeter and length of each side)

  1. Jan 31, 2007 #1
    1. The problem statement, all variables and given/known data
    A city lot has the shape of a right triangle whose hypotehenuse is 7 ft longer that one of the other sides. Perimiter of the lot is 392 ft how long is each side.


    2. Relevant equations
    P = a + b +c = 392

    hypothenuse is c^2 = a^2 + b^2

    so if c is 7ft longer then one of the sides (let's say b)

    then b +7 = c or b = c-7

    a+ c-7 +c = 392
    a +2c = 399
    a = 399 -2c

    To find c I use

    Pythogorian formula but replace a and b with their equivalent of c

    (399-2c)^2 + (c-7)^2 = c^2

    Is it the right way to resolve the problem? if it is, why after 4-5 attempts I keep getting different values of c or sometimes no c at all :)

    If it's the right way to go

    is the (399-2c)^2 + (c-7)^2 = c^2 implies...

    -4c^2 + 1596c + 159201 +c^2 - 14c + 49 = c^2 ? Just to make sure I'm not missing a minus.

    Thank you:)

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 31, 2007 #2

    cristo

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    Your method looks right.

    This should read +4c2+...
     
  4. Jan 31, 2007 #3
    okay this what I get then...
    4c^2 + 1582c + 159250 = 0
    or
    2c^2 + 791c + 79625 = 0 if I divide everything by 2

    c = -b +/- sqrt of(b^2 -4ac) and everything divided by 2a

    however b^2 - 4ac is negative and I can't do a sqrt of a negative number.
    What went wrong?

    791^2 - 4(2)(79625) = 625681 - 637000 = -11319
     
  5. Jan 31, 2007 #4

    cristo

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    There's another mistake in here: this should read 4c2-1596c+...
     
  6. Jan 31, 2007 #5
    What the deuce! It's wichcraft not mathematics! I just solved it
    the sides are c = 175, b = 168 and a = 49

    49^2 + 168^2 = 175^2

    Thank you Cristo, I think your presence in my posts make me think twice harder :)

    Those minuses messed up calculations in the first place :)
     
  7. Jan 31, 2007 #6

    cristo

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    You're welcome!
     
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