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in Perimeter and Area of Plane Figures by (48.0k points)
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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

1 Answer

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by (49.1k points)
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Best answer

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

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