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CAT 2019 Slot 2 — QA Question 4

Geometric CentersEasy

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

Answer & solution

  • A

    80

  • B

    68

  • 72

  • D

    78

Solution


 
As AD and BE are medians, so G is the centroid of ∆ABC.
 
So, AG : GD = BG : GE = 2 : 1.

∴ AG = 8 cm, GD = 4 cm, BG = 6 cm and GE = 3 cm.

If we join centroid with all 3 vertices, we get 3 triangles of equal areas.

∴ Area of âˆ†ABC = 3 × Area of âˆ†ABG

⇒ Area of âˆ†ABC = 3 × (1/2 × 8 × 6) = 72 sq. cm. 

Hence, option (a).

CAT 2019 Slot 2 QA Q4: In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respect — Solution | TheCATExam