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In triangle ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to:

1. 14 cm
2. 16 cm
3. 12 cm
4. 10 cm

Correct answer: 10 cm

Solution

The centroid divides each median in the ratio 2:1, so the vectors of the medians from the centroid have lengths 8 cm and 6 cm. Since the medians are perpendicular, the side opposite the included angle can be found using coordinate geometry or vector relations, giving \(AB = 10\) cm.

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