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16 Jan 2023, 17:29
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Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is
A. 9
B. 12
C. 18
D. 27
E. 36
from beatthegmat
A. 9
B. 12
C. 18
D. 27
E. 36
from beatthegmat
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17 Jan 2023, 00:40
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Attachment:
Screenshot 2023-01-17 at 1.05.48 PM.png
A median divides the area of a triangle into two equal halves. So AD divides ABC into two triangles of area 54 each - triangle ADB and triangle BDC (green = red + yellow)
Now focus on triangle ADB. DE is the median here splits this triangle into further two equal halves of area 27 each - triangle AED and triangle BED.(red = yellow)
Now focus on triangle BED. The centroid divides a median in the ratio 2:1 so BO:OD = 2:1
Since altitude of triangles BEO and DEO is the same, their areas will be in the ratio of the bases BO:OD i.e. their areas will be in the ratio 2:1.
Since area of triangle BED is 27, area of triangle EOD is 9 and that of triangle BEO is 18.
Answer (A)
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