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Question 4 : 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
We know that intersection of two medians is called a Centroid
We know, a Centroid divides the median in the ratio 2:1
AD = 12cms,
AG = 8cms, GD = 4cms
And similarly, BG = 6cms, GE = 3cms
Now, area (ABE) can be easily found out
area (ABE) = x BE X AG
area (ABE) = x 9 x 8 = 36 cm2
area (ABE) = area (BEC)
area (ABC) = 2 x 36 = 72 cm2
The question is "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"
Choice C is the correct answer.
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