Find the perimeter of the triangle #ABC#?

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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=2:1#,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#

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