Question 877777
The legs are x and y.


{{{x^2+y^2=8^2}}} for the Pythagorean Theorem sides relationship, and {{{x+y+8=18}}} for the perimeter.


Perimeter equation goes through
{{{x+y=10}}}
{{{y=10-x}}}
Substituting into right triangle pythagorean thm. equation,
{{{x^2+(10-x)^2=64}}}
{{{x^2+100-20x+x^2=64}}}
{{{-20x+100=64}}}
{{{-20x=64-100}}}
{{{20x=100-64}}}
{{{20x=36}}}
{{{x=36/20=18/10=9/5}}}
{{{highlight(x=9/5)}}}
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Again using just the simplified relationship from perimeter equation,
{{{y=10-9/5}}}
{{{y=50/5-9/5}}}
{{{highlight(y=41/5)}}}