In a triangle ABC, medians AD | Quantitative Aptitude – Geometry
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The question below is from previous year CAT question from CAT 2019 exam comes from CAT Geometry : In a triangle ABC, medians AD. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:
CAT 2019 – Slot -2 - Question 1 - In a triangle ABC, medians AD
Q. 1: 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
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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