The centroid of an equilateral triangle ABC is G and AB

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The centroid of an equilateral triangle ABC is G and AB = 10 cm. The length of AG (in cm) is :

1. 3 1
  3
2. 10
  √3
3. 10√3
  3
4. √3
  3

Correct Option: C

We draw a figure of an equilateral triangle ABC whose G is centroid and AB = 10 cm

BD = DC = 5 cm
∠ADB = 90°
∴ AB² = BD² + AD²
⇒ 10² = 5² + AD²
⇒ 100 = 25 + AD²
⇒ AD² = 100 - 25 = 75
∴ AD = √75 = 5√3

∴ AG =	2	AD =	2	× 5√3 =	10√3	cm.
	3		3		3