Question

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

Answer 1

let ABC be a right triangle in which angle B 90°

then, angle A+angle C=90°
we have: angle B greater than angle A and B greater than angle C
=AC is greater than BC and AC is greater than AB
(side opp. to larger angle is longer)
AC is the longest side
hence,in a right triangle, the hypotenuse is the longest side.

Answer 2

Answer:

In ΔABC, <B = 90

= <A = <B

= BC < AC - - - (1)

= <C < <B

= AB < AC - - - (2)

∴ From the equations (1) and (2) we get that,

=> AC is the longest side.

∴ Ina right angled triangle, the hypotenuse is the longest side.

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