The side of an equilateral Δ ABC = 3 √(7) cm, P is a point on side BC such that BP : PC = 1: 2. The length (in cm) of AP is:

The side of an equilateral Δ ABC = 3 √(7) cm, P is a point…

The side of an equilateral $\Delta$ ABC = 3 $\sqrt{7}$ cm, P is a point on side BC such that BP : PC = 1: 2. The length (in cm) of AP is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 7.

BP : PC = 1 : 2

BP = 1/3 × BC = $\sqrt{7}$

Now in $\Delta$ ABP,

Cos60 = (AB² + BP² - AP²)/(2 × AB × BP)

1/2 = (63 + 7 - AP²)/(2 × 21)

AP = 7 cm.