Question

Perpendiculars are drawn on the sides of an equilateral triangle from any point within the triangle. If the lengths of these perpendiculars be 6 cm, 7 cm and 9 cm, then the length of a side of the triangle is :

(a) \(\frac{44}3\sqrt 3\) cm

(b) \(\frac{11}3\sqrt 3\) cm

(c) \(\frac{22}3\sqrt 3\) cm

(d) \(11\sqrt 3\) cm

Answer 1

Correct option is (a) \(\frac{44}3\sqrt 3\) cm

Let △ABC  be an equilateral triangle.

Length of each side be ′a′ cm

O is a point in the interior of the triangle . 

OX ⊥ BC, OY ⊥ CA and OZ ⊥ AB

Let OZ = 6cm, OX = 7cm and OY = 9cm

Area of △ABC =  Area of △AOB + Area of △BOC +  Area of △COA