In an equilateral triangle O is any point in the interior of the triangle and perpendiculars are dr

Consider an equi lateral Triangle,  O is an iterier point

Now devide triangle in to three partsAOB,BOC, AOC

Sum of the areas of all the three triangles  =   1/2 X BaseX Height  =  1/2  X  a  X(h₁+h₂+h₃)   (1)

Area of the ABC   =3 /4    a²   (2)

Eqaution (1)=(2)

1/2  X  a  X(h₁+h₂+h₃) =3 /4    a²  h₁+h₂+h₃=(3/2) a

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