Question

show that in a right angle triangle, the hypo-tenure is the longest side

Answer 1

Given 
Δ ABC is a right angled triangle and ∠B =90°

To Prove 
AC is longest 

Proof
In Δ ABC
∠A + ∠B +∠C = 180°                    .................. ( angle sum property) 
∠A + 90° +∠C = 180°
∠A + ∠C = 90° 
hence angle cannot be 0
so
∠A will be smaller than 90 
∠A < 90
∠A  < ∠B
BC < AC         ( side opp.. to greater angle are longer )

and ∠C < 90
∠C  < ∠B
AB < AC               ( side opp.. to greater angle are longer )

AC is the longest side in Δ ABC