Question:
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
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
Updated On: Jul 23, 2025
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Correct Answer: 9
Solution and Explanation
We are given the following relationships between areas of triangles:
\(Area \ of \ △ABD : Area \ of \ △BDC = 1 : 1\)
Thus, the area of \(△ABD = 54\)
\(Area \ of \ △EDB : Area \ of \ △ADE = 1 : 1\)
Thus, the area of \(△ADE = 27\)
As a result, O is the centroid, which divides the medians in a \(2:1\) ratio.
\(Area \ of \ △BEO : Area \ of \ △EOD = 2 : 1\)
Now, the area of \(△EOD = 9\)
Final Answer:
The area of \(△EOD\) is \(9\) square cm.
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