Question 5535
{{{a^2 +b^2 = c^2}}}
Let a = shorter leg
Let b = longer leg
let c = hypoteneuse
a is 14 feet shorter than b:
a+14=b
{{{a^2 +b^2 = c^2}}}
we can substitute a+14 in for our b, and use the hypoteneuse value of 26:
{{{(a^2 +(a+14)^2) = 26^2}}}
{{{(a^2 +a^2+28a+196) = 26^2}}}
{{{2a^2+28a+196=676}}}
divide both sides by two:
{{{a^2 +14a+98=338}}}
subtract 338 from both sides:
{{{a^2+14a-240=0}}}
{{{(a+24)(a-10)=0}}}
a=-24 or a=10
we can rule out the -24, because we are talking about a distance, which is always positive:
so the shorter leg = 10 feet
Put this back into the equation:

a+14=b
10+14=24, so the longer leg is 24 feet
and this makes sense because 
10^2 + 24^2= 100 +576 = 676

and 26*26 = 676