A given triangle to be right-angled, if it satisfies Pythagorean Theorem. That is, the sum of the squares of the two smaller sides must be equal to the square of the largest side.
(a- 1) cm, 2√a cm, (a + 1) cm
Longest side = (a + 1) cm
(a + 1)2 = a2 + 2a + 1
and (a – 1)2 + (2 √a )2 = a2 – 2a + 1 + 4a = a2 + 2a + 1
a2 + 2a + 1 = a2 + 2a + 1
It is a right triangle.
