In the figure shown below AD BE and CF are all medians of triangle ABC and GH is parallel to BC If B...........

Quantitative Aptitude ( CCS) Geometry

In the figure shown below AD, BE and CF are all medians of triangle ABC, and GH is parallel to BC. If BH = 10 cm, what is the length (in cm) of AB?

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Explanation:

We use the property that medians of a triangle divide each other in the ratio 2 : 1.
∴ AO : OD = BO : OE = CO : OF = 2 : 1
Now, consider ΔAOH and ΔADB. We can see that they are similar by the AAA property.
∴ Their sides are in the same ratio.
Specifically, AO : AD = 2 : 3 = AH : AB
∴ AH = 2/3 x AB × AB = 2/3 × (AH + BH)
= 2/3 × (AH + 10)
∴ AH = 20 cm
∴ AB = AH + BH = 30 cm