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P IS A POINT ANSIDE AN EQUILATERSL TRIANGLE OF 2010 UNITS.THE SUM OF THE LENGTH OF ALL PERPENDICULARS DRAWN FROM P TO SIDES IS
1.2010
2.2010ROOT3
3.1005ROOT3
4.2010/ROOT3
As this sum is independent of position of P,
Consider P to be on one of the vertices.....
Hence sum = length of altitude = {root(3)/2}*a
Option 3.
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