Question 1074153
Legs, x and 2x
longest side, r



{{{x+2x+r=28}}}
{{{3x+r=28}}}



{{{x^2+(2x)^2=r^2}}}
{{{x^2+4x^2=r^2}}}
{{{5x^2=r^2}}}


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{{{5x^2=(28-3x)^2}}}
{{{5x^2=28^2-6*28x+9x^2}}}
{{{0=28^2-6*28x+4x^2}}}
{{{x^2-42x+7*28=0}}}


{{{x=(42+- sqrt(980))/2}}}

{{{x=(42+- sqrt(49*2*2*5))/2}}}

{{{x=(42+- 14sqrt(5))/2}}}

{{{x=21+- 7*sqrt(5)}}}



The MINUS form:
x is 5.348, 2x is 10.695, r is 11.956
check:  5.348^2+10.695^2=11.956^2
142.98 = 142.95


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LEG: {{{highlight(x=21-7sqrt(5))}}}
.
Other LEG:  {{{highlight(2x=42-14*sqrt(5))}}}
.
{{{r=28-(21-7sqrt(5))-(42-14sqrt(5))}}}
HYPOTENUSE:  {{{highlight(r=-35+21*sqrt(5))}}}, about 11.957
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The PLUS form:
x is 36.6.... No.  This does not work.