From a point in the interior of an equilateral triangle,

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From a point in the interior of an equilateral triangle, the perpendicular distance of the sides are √3cm, 2√3cm and 5√3 cm. The perimeter (in cm) of the triangle is

1. 64
2. 32
3. 48
4. 24

Correct Option: C

Using Rule 1,

Let ABC be an equilateral triangle of side x cm.
Also, Let OD = √3 cm,
OE = 2√3 cm and OF = 5√3 cm.
From the figure, ar. ∆BOC + ar. ∆AOC + ar. ∆AOB = ar. ∆ABC

or,	1	× x × √3 +	1	x × 2√3 +	1	× x ×5√3 =	√3	x²
	2		2		2		4

or, 2√3 + 4√3 + 10√3 = √3x
or, x = 2 + 4 + 10 = 16
∴ Perimeter of the triangle = 3x = 3 × 16 = 48 cm