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hexagon

by shashank.ism » Tue Feb 09, 2010 1:00 pm
ABCDEF is a regular hexagon of side a. P is a point inside the hexagon. If PG, PH, PI, PJ, PK, PL
are drawn perpendicular to the sides AB, BC, CD, DE, EF, FA, respectively, then the value of
PG + PH + PI + PJ + PK + PL is equal to

6Sqrt(3)a
3Sqrt(3)a
3a
6a
None of these
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by sparky_paris » Thu Feb 11, 2010 5:25 pm
3 sqrt 3 a option B
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by harsh.champ » Thu Feb 18, 2010 10:23 am
shashank.ism wrote:ABCDEF is a regular hexagon of side a. P is a point inside the hexagon. If PG, PH, PI, PJ, PK, PL
are drawn perpendicular to the sides AB, BC, CD, DE, EF, FA, respectively, then the value of
PG + PH + PI + PJ + PK + PL is equal to

6Sqrt(3)a
3Sqrt(3)a
3a
6a
None of these
The perpendicular can be drawn through the mid-pt. of the hexagon[I am taking the centre as the above sum will always be constant any pt. you take]

Thus, the answer will be 6 X length of the altitude.
Now,the perpendicualr frm centre will bisect the side[since we have a regular hexagon]
So,length of altitude = sqrt ( a^2 - (a/2)^2 )
=sqrt(3) x (a/2)
Thus the answer = [spoiler]6 x [ sqrt(3) x (a/2) ] = 3Sqrt(3)a.Hence B.[/spoiler]
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by shashank.ism » Fri Feb 19, 2010 11:03 am
Yeah you both are correct and Correct Ans is B
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