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Equilateral Triangle 123 (Posted on 2007-09-05) Difficulty: 3 of 5
An equilateral triangle lies with its three vertices at respective distances from the origin as 1, 2 and 3 units. What is the length of each side of the triangle?

  Submitted by Charlie    
Rating: 4.0000 (3 votes)
Solution: (Hide)
Without loss of generality, one vertex can be at (0,1).

The distance of each of the other two points from the vertex, and the equality of the distances from each other, yield four equations, in the four unknowns of two x coordinates and two y coordinates.

When these are solved, and the other vertices are placed at (sqrt(27)/2, 3/2) and (sqrt(3),-1), the conditions are met and the length of each side is sqrt(7).

Comments: ( You must be logged in to post comments.)
  Subject Author Date
AnswerK Sengupta2008-10-21 00:59:41
SolutionSolutionBractals2007-09-05 10:43:23
Cheating - Interested in the Mathsbrianjn2007-09-05 09:50:22
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