Where is the Store?


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?

Hints and discussion.


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.

 


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