Use the formulas a = x 2 – y 2, b = 2xy, c = x 2 + y 2 to answer this question. one leg of a right triangle has length 11 and all sides are whole numbers. find the lengths of the other two sides.
the other leg =
and the hypotenuse =

This is the concept of Pythagorean theorem which states that:
a^2+b^2=c^2
but from the question;
a=x^2+y^2
b=2xy
c=x^2+y^2
therefore substituting the values of a.b and c in our formula we get,
(x^2+y^2)^2+(2xy)^2=(x^2+y^2)^2
x^4-2x^2y^2+y^4+4x^2y^2=x^4+2x^2y^2+y^4
Checking on the difference for squares we consider 1,4,9,16,36,49,64,81,...
given that one of the legs is 11, to get the other leg we look for the square difference of two minimum numbers that will give us 11^2=121
we have;
11^2+60^2=61^2
therefore the answer is:
a=11,b=60 and c=61