△ ABC is an equilateral triangle with side 18 cm. D is a point on BC such that BD = 1/2 BC. Then lenght (in cm) of AD is :

△ ABC is an equilateral triangle with side 18 cm. D is a…

△ ABC is an equilateral triangle with side 18 cm. D is a point on BC such that BD = $\frac{1}{2}$ BC. Then lenght (in cm) of AD is :

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 6√7

In ΔABD

CosB = (AB² + BD² - AD²)/(2 × AB × BD)

Cos60° = (182 + 62 - AD²)/(2 × 18 × 6)

1/2 = (324 + 36 - AD²)/216

216 = 648 + 72 - 2AD²

2AD² = 648 + 72 - 216

AD² = 252

AD = 6√7