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G is the centroid of ∆ ABC. The medians AD and BE intersect at right angles. If the lengths of AD and BE are 9 cm and 12 cm respectively; then the length of AB (in cm) is
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- 9.5
- 10
- 11
- 10.5
- 9.5
Correct Option: B
Firstly , We draw a figure of triangle ABC whose G is the centroid ,
AD = 9 cm.
| ∴ AG = | × 9 = 6 cm | |
| 3 |
BE = 12 cm.
| ∴ BG = | × 12 = 8 cm | |
| 3 |
∠AGB = 90°
∴ From ∆ ABG,
AB = √AG² + BG²
AB= √6² + 8²
AB = √36 + 64
AB = √100 = 10 cm.
