Intermath | Workshop Support


The Third Side

Problem Statement
The lengths of two sides of a triangle are 5 and 11. If the length of the third side is also a whole number, what are the smallest and largest possible perimeters that the triangle can have?


Investigation/Exploration of the Problem

Using the theorem that states the sum of two sides must be greater than the length of the third side, the possibilities for the third side are between 6 and 16. The problem is restricted to whole numbers so the smallest side could be 7 and the largest possible side is 15.



Case 1




Case 2





Using Geometer’s sketchpad – I learned how to construct a triangle with sides of 5 and 11. I then set point D in motion. This was a great visual representation. It showed the triangle degenerating into a straight line when the third side had measurements of 6 and 16.



Author & Contact
Dottie Mitcham



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