Question 1074446
*[illustration se3.png].
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By Pythagoras,
{{{(x+6)^2+(y+6)^2=20^2}}}
By similar triangles,
{{{y/6=(y+6)/(x+6)}}}
So,
{{{6(y+6)=y(x+6)}}}
{{{(x+6)=(6(y+6))/y}}}
{{{(x+6)^2=(36(y+6)^2)/y^2}}}
Substituting,
{{{(36(y+6)^2)/y^2+(y+6)^2=400}}}
{{{36(y+6)^2+y^2(y+6)^2=400y^2}}}
{{{36(y^2+12y+36)+(y^4+12y^3+36y^2)=400y^2}}}
{{{(36y^2+432y+1296)+(y^4+12y^3+36y^2)=400y^2}}}
{{{y^4+12y^3+72y^2+432y+1296=400y^2}}}
{{{y^4+12y^3-328y^2+432y+1296=0}}}
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*[illustration f9.JPG].
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Graphing finds two positive solutions,
{{{y=3.04}}} and {{{y=11.84}}}
with corresponding x values,
{{{(x+6)=(6(y+6))/y}}}
{{{x=11.84}}} and {{{x=3.04}}}
So then the lengths of the other sides are,
{{{x+6=17.84}}}{{{cm}}}
{{{y+6=9.04}}}{{{cm}}}