Question 623408
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)}}}

this is the work that I had done:
{{{a^2+b^2=c^2}}}

{{{x^2+((1/2x)+11)^2=(2x+1)^2}}}
simplified: {{{x^2+(1/4x^2)+11/x+121=4x^2+4x+1}}} ***** 11^2 = 121, and 11/x
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{{{x^2+(1/4x^2)+11/x+121=4x^2+4x+1}}}
Multiply by 4x^2 to eliminate the fraction
{{{4x^4 + 1 + 44x + 484x^2 = 16x^4 + 16x^3 + 4x^2}}}
{{{12x^4 + 16x^3 - 480x^2 - 44x - 1 = 0}}}
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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?
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written in standard form: {{{(11/4x^2)+7x+110=0}}}

multiply everything by (11/4): {{{x^2+(28/11x)-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.