Three towns in Ireland -- Poole, Bray, and Alton -- are located 8, 3, and 5 miles, respectively, from a store. How far apart are the towns from one another if they are located at the vertices of an equilateral triangle?

You may want to make a GSP file to model the situation.

Hints/Solution:Is the store inside, on, or outside the triangle?

Comments:Compare with the

Barnproblem (Distance from the Nearest Road).

Extensions/Variations:Consider the problem if the three distances are 5, 7, and 8 units.

Consider the problem if the three distances are 1, 2, and 3 units (Sastry, 1997).

References:Hunter, J. A. H.

100 Mathematics Problems;Problem #99.

Sastry, K. R. S. (1997) Problem proposal 340.Mathematics and Computer Education, 31,p. 195.

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