Question 98133
c=hypotenuse 
b=shorter leg 
a=longer leg
{{{(b+2)^2+b^2=(b+6)^2}}}
{{{b^2+4b+4+b^2=b^2+12b+36}}} subtract the left from the right. {{{0=-b^2+8b+32}}}
multiply -1 times both sides {{{b^2-8b-32=0}}}
quadratic formula: b=10.928... (b=-2.928... is extraneous)
a=b+2=12.928...
c=b+6=16.928...
Ed