Question 739103
c=24

Clearly the side we know the least about is the shortest so...

a=x

the length of one leg is 6 feet more than the other means...

b=x+6

So our equation is:

{{{x^2+(x+6)^2=24^2}}}

so here we go...

{{{x^2+(x^2+12x+36)=576}}}


{{{2x^2+12x-540=0}}}

divide by  2...

{{{x^2+6x-270}}}


but this quadratic cannot be factored - so we use the quadratic formula

{{{x = (-6 +- sqrt( 6^2-4*1*(-270) ))/2 }}} 



From which the negative solution can be discarded (why?)

therefore...

{{{x=3sqrt(31)-3}}}

and so...

{{a=3sqrt(31)-3}}}

{{b=3sqrt(31)+3}}}

{{{c=24}}}