Question

show that in a right angled triangle the hypotenuse is longest side

Answer 1

Let there is a right angle triangle ABC where

AB is the perpendicular, AC is hypotenuse and BC is the base of the triangle.

From Pythagoras Theorem,  

     hypotenuse2 = Perpendicular2 + base2

=> AC2 = BC2 + AB2

=> AC = √(BC2 + AB2

)

So hypotenuse is the longest side in a right angle traingle.