Question

in a right angle triangle prove that the hypotenuse is the longest side

Answer 1

Length of side opposite to greater angle is greater

in a right angled triangle one angle is 90 and other are smaller than 90

so hypotenuse is opposite to 90 and thus the longest

Answer 2

In the given triangle ABC,

Angle B = 90°

Hence Angle A + Angle C = 180°- 90°  ...(Sum of all angles of the triangle are 180°)

Therefore Angle B is the greater angle than Angle A and Angle C. [Angle A>Angle C ]  

We know that, Side opposite to greater angle is always longer.

Therefore, Side opposite to angle B is AC

.

[AC > BC and AC > AB]

That is AC is the longest side..

[AC is the hypotenuse] ...