From a point within an equilateral triangle, perpendiculars

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From a point within an equilateral triangle, perpendiculars drawn to the three sides, are 6 cm, 7 cm and 8 cm respectively. the length of the side of the triangle is :

Let ABC be equilateral triangle of side a cm and P be a point inside it.

From the figure, Area of ∆APB + Area of ∆PBC + Area of ∆APC = Area of ∆ABC

⇒	1	× a × 6 +	1	× a × 7 +	1	× a × 8 =	√3	a²
	2		2		2		4

⇒	1	a (6 + 7 + 8) =	√3	a²
	2		4

⇒	21a	=	√3	a²
	2		4

⇒ a =	21	×	4	= 14√3 cm.
	2		√3