Suppose a triangle has sides of length a, b and c.
Show that there exists a triangle with sides of length , and .
The lengths r, s and t form the sides of a triangle if and only if the
longest length is less than the sum of the other two lengths.
Suppose in our case that c is the longest length.
Let a = A2, b = B2 and c = C2. Then:
A2 + B2 > C2
As a result:
(A + B)2 = A2 + B2 + 2AB > C2 + 2AB
(A + B)2 > C2
since 2AB is positive.
A + B > C