Quantitative Aptitude – Geometry – Triangle – In a triangle ABC, medians AD


Slot – 2 – Quantitative Aptitude – Geometry – Triangle – In a triangle ABC, medians AD

Q. 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. 80
  2. 68
  3. 72
  4. 78
Answer: 72

Solution:

Draw the third median CF. As We know that the :
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 triangle having equal area.
So Area of Triangle ABC = 6* Area of one small triangle—————-1)
Now Given AD = 12 and GD:AG = 1:2 So GD = 1/3 *12 =4
BE = 9 and BG:GE = 2:1 So BG = 2/3 *9 = 6
As BG is perpendicular to GD,
Area of triangle BGD = ½ ×GB × GD = ½ × 6 × 4 =12
Hence, from eq 1) area of triangle ABC = 6 × 12 = 72


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