What is the perpendicular distance from the third side to the point?

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1 Answer
CW
Jun 20, 2018

Option #E. " " 3#

Explanation:

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Let #|ABC|# denote area of #DeltaABC#
#AD=h=AB*sin60=4sqrt3*sqrt3/2=6#
#|ABC|=|APB|+|BPC|+|CPA|#
#=> 1/2*BC*AD=1/2*AB*PE+1/2*BC*PF+1/2*CA*PG#
#=> 1/2*4sqrt3*h=1/2*4sqrt3*x+1/2*4sqrt3*z+1/2*4sqrt3*y#
#=> h=x+z+y#
#=> 6=x+z+y#
given that #x=2/3, and y=7/3#,
#=> z=6-2/3-7/3=6-9/3=3#

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