Question

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

Answer 1

Let ABC is a right angle triangle AC is hypotenuse

to show i) AC > AB

ii) AC > BC

$\Delta ABC$

$\angle ABC={90}^{\circ }$

$\angle ABC+\angle BAC+\angle ACB={180}^{\circ }$

$\angle BAC$ & $\angle ACB$ are acute angle.

$\angle BAC<{90}^{\circ }$ & $\angle ACB<{90}^{\circ }$

$\angle BAC<\angle ABC$ & $\angle ACB<ABC$

$\therefore BC<AC$ & $ABC<AC$ proved