SOLUTION: hello there, I'm having trouble finding the lengths of this triangle whose measurements are as follows: short leg={{{x}}} long leg={{{((1/2x)+11)}}} hypotenuse={{{(2x+1)}}} t

Algebra ->  Algebra  -> Triangles -> SOLUTION: hello there, I'm having trouble finding the lengths of this triangle whose measurements are as follows: short leg={{{x}}} long leg={{{((1/2x)+11)}}} hypotenuse={{{(2x+1)}}} t      Log On

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Question 623408: hello there, I'm having trouble finding the lengths of this triangle whose measurements are as follows:
short leg=x
long leg=%28%281%2F2x%29%2B11%29
hypotenuse=%282x%2B1%29
this is the work that I had done:
a%5E2%2Bb%5E2=c%5E2
x%5E2%2B%28%281%2F2x%29%2B11%29%5E2=%282x%2B1%29%5E2
simplified: x%5E2%2B%281%2F4x%5E2%29%2B11x%2B111=4x%5E2%2B4x%2B1
written in standard form: %2811%2F4x%5E2%29%2B7x%2B110=0
multiply everything by (11/4): x%5E2%2B%2828%2F11x%29-40=0
And now I'm stuck here, as you can see, there's no way I can factorize this, what have I done wrong?
Your help is very much appreciated.
Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
hello there, I'm having trouble finding the lengths of this triangle whose measurements are as follows:
short leg=x
long leg=%28%281%2F2x%29%2B11%29
hypotenuse=%282x%2B1%29
this is the work that I had done:
a%5E2%2Bb%5E2=c%5E2
x%5E2%2B%28%281%2F2x%29%2B11%29%5E2=%282x%2B1%29%5E2
simplified: x%5E2%2B%281%2F4x%5E2%29%2B11%2Fx%2B121=4x%5E2%2B4x%2B1 ***** 11^2 = 121, and 11/x
========================
x%5E2%2B%281%2F4x%5E2%29%2B11%2Fx%2B121=4x%5E2%2B4x%2B1
Multiply by 4x^2 to eliminate the fraction
4x%5E4+%2B+1+%2B+44x+%2B+484x%5E2+=+16x%5E4+%2B+16x%5E3+%2B+4x%5E2
12x%5E4+%2B+16x%5E3+-+480x%5E2+-+44x+-+1+=+0
-------------------
Using graphical or numerical approximations,
x =~ 5.71342
That's the only real number solution.
You sure it's not (1/2)x + 11 for one leg?
=================
written in standard form: %2811%2F4x%5E2%29%2B7x%2B110=0
multiply everything by (11/4): x%5E2%2B%2828%2F11x%29-40=0
And now I'm stuck here, as you can see, there's no way I can factorize this, what have I done wrong?
Your help is very much appreciated.