I am trying to solve what must be a ridiculously simple problem involving Pythagoras’ theorem and some simple geometry but I seem to be missing something. The problem is this:
A farmer has a square field and has set up a drinking trough at a point in the middle of the field that is 50m from one corner of the field, 30m from another corner, and 40m from a third corner (the diagram shows the configuration). The goal is to find the size of the field (either the area of the length of one side – it is a square field).
Note that the 30m and 50m lines do not make the diagonal line of the square field.
I have constructed several right angled triangles and looked for common sides to try and solve simultaneous equations but I end up with 3 equations and 4 unknowns and am thus unable to solve this.
Any help (especially in the form of a detailed explanation) would be greatly appreciated. By the way, I am not a student with a homework assignment – this is a problem I came across and am embarrassed that at my age I cannot figure it out!