Point inside a triangle.

Posted on 2005-04-16
Last Modified: 2008-01-09
Point P is inside equilateral triangle ABC such that AP = 3, BP
= 4 and CP = 5. What is the length of a side of the triangle?

How might I find this out?

Question by:StormyWaters
    LVL 31

    Accepted Solution

    This is a classic and non-trivial puzzle that requires a diagram, the answer is

    √(25 + 12√3)

    Here are a couple of links.
    LVL 27

    Assisted Solution

    First draw a diagram of the problem roughly to scale. Lable all parts which you can. All the sides of the triangle are the same, call that length x. Remember that the angles of the triangel are 60 degrees. Note that you have three internal triangles and that there are relationships betwen their angle. If these hints are not enough write back with the place you are stuck
    LVL 31

    Expert Comment

    sorry answer is

    sqrt( 25 + 12sqrt(3))  =  6.7664
    LVL 13

    Author Comment

    Thank you both for your help.

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