the hypotenuse of a right triangle is 24 ft long. the length of one leg is 6 feet more than the other. find the length of the legs.

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: 
 
so here we go... 
 

 
divide by 2... 
 

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


From which the negative solution can be discarded (why?) 
therefore... 
 
and so... 
{{a=3sqrt(31)-3}}} 
{{b=3sqrt(31)+3}}}