Question

in a right angled triangle show that its hypotenuse is longer

Answer 1

In a right angled triangle ABC let:-

AB=height

BC=base

AC=hypotenuse

By Pythagoras theorem:-

AC²=BC²+AB²

We know that the length of AB and BC cannot be zero.

We also know that if:

x²=y²+z²

In a triangle : AC<AB+BC.

x<y+z.

x>y and x>z provided that they are natural numbers.

This proves that the hypotenuse is the longest side.

Hope it helps.