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:

Question

UPSC Quizroom · Accepted Answer

Let O be the centroid of triangle ABC. Then:

BO : OD = 2 : 1

CO : OE = 2 : 1

Area ratios involving triangles formed with the centroid:

Area(BOC) : Area(ODC) = 2 : 1

Area(COB) : Area(OEB) = 2 : 1

Since BD is a median, Area(BDA) = Area(BDC)

Let Area(AEOD) = 2x → Then total areas sum as:
2x + x + x + 2x = 108 → 6x = 108 → x = 18

So Area(AEOD) = 2x = 36

Since ED joins midpoints of AB and AC, Area(AED) = ¼ Area(ABC) = ¼ × 108 = 27

Finally, Area(EOD) = Area(AEOD) - Area(AED) = 36 - 27 = 9 sq. cm

Answer: 9 sq. cm

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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:

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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:

Options

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