Question

prove that hypotenus is longest side in right angled triangle

Answer 1

According to the Pythagorean Theorem, a^2 = c^2 - b^2. If a^2 can be equal to c^2 - b^2 and b^2 = c^2 - a^2 it means that c^2 is greater than both of them since side length can only be positive. 

Answer 2

According to Pythagoras Theorem 
(Base)² + (Perpendicular)² = (Hypotenuse)²

So Hypotenuse is the sum of the Base and Perpendicular so it is the largest of all sides.