Title
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.
Algebraically
Case 1
5+11>x
16>x
Case 2
5+x>11
x>6
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
