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

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Agam answered 3 month(s) ago

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

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

Class-IX Maths

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Asked by Uday

Jan 2

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Ramesh , SubjectMatterExpert

Member since Apr 01 2014

Sol:

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 = 6 cm, OX = 7 cm and OY = 9 cm
 
Area of ∆ABC = Area of ∆AOB + Area of ∆BOC + Area of ∆COA
 
√3/4 a2 = (1/2 x OZ x AB) + (1/2 x OX x BC) + (1/2 x OY x AC)
 
√3/4 a2 = (1/2 x 6 x a) + (1/2 x 7 x a) + (1/2 x 9 x a)
 
√3/4 a2 = 3a + 7/2 a + 9/2 a
 
√3/4 a2 = 11 a
 
a = (11 x 4) / √3
 
a = 44 / √3 cm = 44√3 / 3 cm.
 
Therefore, the length of the side = 44√3 / 3 cm.

I hope it is clear for you. Ask me if you have any doubts.