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
- 68
- 72
- 78
- 80
Correct Answer: Option: 2
Refer to the figure below:
Draw the third median CF. We know the following facts:
1. The intersection point of medians i.e. centroid (G) divides each median into 2:1.
2. All three medians divide the triangle into 6 parts of equal area.
$GD=\frac{1}{3}\times AD=\frac{1}{3}\times 12=4$
$GB=\frac{2}{3}\times BE=\frac{2}{3}\times 9=6$
Area of triangle BGD = $\frac{1}{2}\times GB\times GD=\frac{1}{2}\times 6\times 4=12$
Hence, area of triangle ABC = $6\times 12=72$
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