Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

O≡(0,0), A≡(2,0)AND B≡(1,√3). P(x,y)

  1. Aug 16, 2009 #1
    consider a triangle OAB formed by O≡(0,0), A≡(2,0)AND B≡(1,√3). P(x,y) is an arbitrary interior point of the triangle moving in such a way that the sum of its distances from the three sides of the triangle is √3 units . find the area of the region representing possible positions of the point P .
     
  2. jcsd
  3. Aug 16, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi abhishek! :wink:

    (this is an equilateral triangle, of course, and one of the possible positions of P is its centroid)

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
  4. Aug 27, 2009 #3
    Re: area

    the triangle is an equilateral triangle, so the distance from any arbitrary point P inside the triangle to the sides of the triangle is constant (and equal to the height of the triangle, so √3 units in this case).

    proof:

    consider P, an arbitrary point inside the triangle.

    http://img148.imageshack.us/img148/5082/triangleo.png [Broken]

    the area of the triangle OAB is √3 units and it is also the sum of the areas of the triangles POA= (d1*0A)/2, POB=(d2*OB)/2 and PAB=(d3*AB)/2.
    but OA=OB=AB=2 units.

    So the sum of the areas of the smaller triangles is d1+d2+d3=√3. Hence, the sum of the distances from P to the sides of the triangle is constant and equal to √3.

    q.e.d.

    so the area of the region representing possible positions of the point P that satisfy the given positions is the area of the triangle = √3 square units...
     
    Last edited by a moderator: May 4, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: O≡(0,0), A≡(2,0)AND B≡(1,√3). P(x,y)
  1. X^3 -x -x^3=0 puzzle (Replies: 4)

  2. 0/0 = ? (Replies: 69)

  3. 0/0 Solved (Replies: 67)

  4. Google gives 0^0=1 (Replies: 24)

Loading...