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In triangle ABC, the medians AD and CF meet at the centroid G and are mutually perpendicular there. If BC = 3 cm and AB = 4 cm, find the length of AC (in cm).

1. sqrt(5)
2. sqrt(6)
3. 2
4. sqrt(7)

Correct answer: sqrt(5)

Solution

A standard result: if the medians from vertices A and C are perpendicular, then b² (the side AC) satisfies AB² + BC² = 5*AC². Substitute the given lengths.

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