Question 985029
Interpreting legs as separate from the hypotenuse,

x and y the legs
{{{x+y=30}}}


{{{y=30-x}}}
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{{{x^2+(30-x)^2=25^2}}}
{{{x^2+900-60x+x^2-625=0}}}
{{{2x^2-60x+275=0}}}


{{{Discriminant=3600-4*2*275=3600-8*275=1400}}}
{{{1400=10*10*14}}}
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{{{sqrt(10*10*14)=10sqrt(14)}}}
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{{{x=(60+- 10sqrt(14))/4}}}


{{{highlight(x=(30+- 5sqrt(14))/2)}}}-----either of these is x and the other is y.