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In a \( \Large \triangle ABC, \angle A : \angle B : \angle C = 2 : 4 : 3 \). The shortest side and the longest side of the triangles are respectively.

A) AC and AB
B) AC and BC
C) BC and AC
D) AB and AC

Correct Answer:



C) BC and AC

Description for Correct answer:

Let \( \Large \angle A = 2x \)

\( \Large \angle B = 4x \)

and \( \Large \angle C = 3x\)

We know, \( \Large \angle A \) + \( \Large \angle B \) + \( \Large \angle C \)= \( \Large 180 ^{\circ} \)

\( \Large \therefore 2x + 4x + 3x = \Large 180 ^{\circ} \)

=> \( \Large 9x = \Large 180 ^{\circ} \)

=> \( \Large x = \Large 20 ^{\circ} \)

Now, \( \Large \angle A = 40 ^{\circ} \)

\( \Large \angle B = 80 ^{\circ} \)

and \( \Large \angle C = 60 ^{\circ} \)

Hence, the shortest side of triangle = side opposite to the smallest angle

= BC and the longest side of triangle = side opposite to the longest angle = AC.

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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