Question 350112
Let x and y be the legs of the triangle.
{{{A=(1/2)xy=24}}}
1.{{{xy=48}}}
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2.{{{x^2+y^2=12^2}}}
Find the intersection points between these two functions.
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{{{drawing(300,300,-2,18,-2,18,circle(11.21,4.28,0.3),circle(4.28,11.21,0.3),graph(300,300,-2,18,-2,18,48/x,sqrt(144-x^2)))}}}
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From eq. 1,
{{{y=48/x}}}
{{{y^2=2304/x^2}}}
Substitute into eq. 2,
{{{x^2+2304/x^2=144}}}
{{{x^4-144x^2+2304=0}}}
{{{x^4-144x^2+5184+2304=5184}}}
{{{(x^2-72)^2+2304=5184}}}
{{{(x^2-72)^2=2880}}}
{{{(x^2-72)^2=64*9*5}}}
{{{x^2-72=0 +- 8*3*sqrt(5)}}}
{{{x^2=72 +- 24sqrt(5)}}}
or approximately,
{{{x1=11.21}}} and {{{x2=4.28}}}
with corresponding y values of 
{{{y1=4.28}}} and {{{y2=11.21}}}