Question

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

• A. 68
• B. 72
• C. 78
• D. 80

Answer 1

The Correct Option is B

From the figure

Sketch the third median CF. It is noted that:

The point of intersection of medians, known as the centroid (G), divides each median into a 2:1 ratio.

All three medians collectively partition the triangle into six equal areas.
\(GD=\frac{1}{3}×AD=\frac{1}{3}×12=4\)

\(GB=\frac{2}{3}×BE=\frac{2}{3}×9=6\)
Area of triangle BGD =\(\frac{1}{2}\times GB\times GD=\frac{1}{2}\times6\times4=12\)
Hence, area of triangle \(ABC = 6×12=72\)