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CAT 2019 Quant Question with Solution 50

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

  1. 68
  2. 72
  3. 78
  4. 80
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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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