Question

Show that in a right triangle, the hypotenuse is the longest side

Answer 1

Let $ABC$ be the right angled triangle in which $\angle B={90}^o$

$\therefore \angle A+\angle C={90}^o$

Since sum of all the angles of a triangle $={180}^o$ [angle sum property]

$\angle B=\angle A+\angle C$

$\Rightarrow \angle B>\angle A$

and $\angle B>\angle C$

$\Rightarrow AC>BC$

$\therefore$ Side opposite to greater angle is longer and $AC>AB$

$\therefore AC$ is the longest side, i.e hypotenuse is the longest side.