Find the perimeter of the triangle ABCABC?

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1 Answer
P dilip_k
Feb 7, 2018

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Since orthocenter divides the normals in the ratio (2x)/sqrt3:x/sqrt3=2:12x√3:x√3=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=(2x)√3+x√3=(3x)√3=3√3x,

If aa be the length of each side then
sqrt3/2*a=3sqrt3x√32⋅a=3√3x

=>a=6x⇒a=6x

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

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