Question 73992
The word problem translates to 
{{{a=3+b}}}"...one leg (a) is (=) 3 more (+) than another leg (b)"
So plug this into Pythagoreans theorem
{{{a^2+b^2=c^2}}}where a and b are the legs and c is the hypotenuse.
{{{(3+b)^2+b^2=15^2}}}Plug in 3+b into a, this eliminates a
{{{9+6b+2b^2=225}}}Add like terms and simplify. 
{{{2b^2+6b+9-225=0}}}Subtract 225 from both sides
{{{2b^2+6b-216=0}}}
Now use the quadratic formula to solve for b
*[invoke quadratic "b", 2, 6, -216 ]
Disregard the negative answer (a negative length doesn't make any sense). So the length of one leg is 9 in. Use this to find the other leg.
{{{a=3+b}}}
{{{a=3+9}}}
{{{a=12}}}
So the other leg is 12 in.
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Check:
{{{a^2+b^2=c^2}}}
{{{12^2+9^2=15^2}}}
{{{144+81=225}}}
{{{225=225}}}Works