In a triangle ABC, medians AD and CE are drawn. If AD = 5, … | CGP Edu

Maths Trigonometrical Equations and in Equations, Properties of Triangles, Height and Distance Relation Between Sides and Angles, Solutions of Triangles Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

In a triangle ABC, medians AD and CE are drawn. If AD = 5, ∠ DAC = , the area of triangle ABC is -

A

15/7

B

25/3

C

25/6

D

None of these

Text Solution

Verified by Experts

The correct answer is:

Let O be the point of intersection of the medians of triangle Δ ABC shown in the figure. Then the area of Δ ABC is three times that of Δ AOC, because O being the centroid of Δ ABC.

It divides of median through B in the ratio 2 : 1 and the height of Δ AOC is one-third that of Δ ABC

Now, in Δ AOC, AO = 10/3 AD = 10/3.

Applying the sine rule to Δ AOC, we get

=

⇒ OC =

∴ Area of Δ AOC = . AO . OC. sin ∠ AOC

= .sin

= . = =

⇒ Area of ABC = = .

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