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# Point inside a triangle.

Posted on 2005-04-16
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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?

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Question by:StormyWaters

LVL 31

Accepted Solution

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

&#8730;(25 + 12&#8730;3)

Here are a couple of links.

http://mathcentral.uregina.ca/QQ/database/QQ.09.96/Pisco1.html
http://www.kalva.demon.co.uk/sweden/sol/sol772.html
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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
0

LVL 31

Expert Comment

sqrt( 25 + 12sqrt(3))  =  6.7664
0

LVL 13

Author Comment

Thank you both for your help.
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