Question

Show that in an right angle triangle the hypotenuse is the longest side

Answer 1

abcd is a right angle triangle at b.
(using inequalities)
the greatest angle has the greatest side apposite to it.
so, in a right angle triangle the greatest angle is 90°. so the line opposite to it (hypotenuse) is the longest side.


I hope you understand it well.

Answer 2

$\huge\mathfrak{Answer}$

Here Given that : A right angled triangle ABC, $\angle$B = 90°.

To prove : Hypotenuse AC is the longest wide.

Means

AC > AB

AC > BC

Now in $\triangle$ABC

$\angle$ = 90°

But $\angle$CAB + $\angle$BCA + $\angle$CBA = 180°

90° + $\angle$BCA + $\angle$CAB = 180°

=> $\angle$BCA + $\angle$CAB = 90°

=> $\angle$BCA and $\angle$CAB are acute angles

Thus, $\angle$BCA < 90° and $\angle$CAB < 90°

=> $\angle$BCA < $\angle$ABC and $\angle$CAB < $\angle$ABC

=> AC > AB and AC > BC

Side opposite to greater angle is larger. Thus, AC is the longest side.

#Answerwithquality

#BAL