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 Equilateral Triangle (Posted on 2003-12-18)
Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.
Then find the length of the side of the equilateral triangle.

 No Solution Yet Submitted by Ravi Raja Rating: 4.0000 (5 votes)

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 a solution? | Comment 1 of 19
I'm sure there's a better way to do this, but while I was looking at the problem, I noticed the lengths of the lines that are drawn from P to triangle vertices are proportionate. I then cheated like a madwoman and realized that 4 is the length needed for each segment to meet in the center of the triangle. I drew an imaginary line from the middle of one the sides of the triangle to P, and had a 30-60-90 triangle. Two times the langth of s times the square root of three should be the answer. 8[3^(1/2)]
 Posted by Rachel on 2003-12-18 08:59:48

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