Question

show that in a right angle triangle the hypotenuse is the longest side ​

Answer 1

Answer

Let ABC be a right angle triangle such that angel ABC = 90° .

We know that ,

• $\angle{abc} + \angle{bca} + \angle{cab} = 180 \degree$

=> 90° + \_ bca + \_ cab = 180°

=> \_ bca + \_ cab = 180°-90°

=> \_ bca + \_cab = 90°

from above ,

we have \_ bca and \_ cab are the acute angels .

• => \_ bca < 90°

and \_cab < 90°

• => \_ bca < \_ abc

and \_ cab < \_ abc

=> ab < ac and bc < ac

( side opposite to Greater angle is longer )

Hence , the hypotenuse AC is the longest side .