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 Barn problem (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.