Find the perimeter of the triangle ABC?

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1 Answer
Feb 7, 2018

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Since orthocenter divides the normals in the ratio (2x)/sqrt3:x/sqrt3=2:1,so the normals must be medians here. It is only possible for equilateral triangle.

Hence height of the equilateral triangle will be

=(2x)sqrt3+xsqrt3=(3x)sqrt3=3sqrt3x,

If a be the length of each side then
sqrt3/2*a=3sqrt3x

=>a=6x

So perimeter of the triangle =3×6x=18x