Posted by JV on .
Assume that the sides of triangles are limited to
whole-number measures. How many different
triangles have a perimeter of 12 meters? Explain
how you determined this.
The constraints are as follows:
any two sides of a triangle must be longer than the third side, so 1,6,5 because 1+5=6 (not greater) would not work, nor 2,2,8, because 2+2<8, etc.
So make a table of sides, and cross out the ones that do not work.
The sides a, b and c must be in ascending order so that you do not repeat the same triangles.
So the method of solution is by tabulation.
a b c OK?
1 4 7 X
1 5 6 X
2 4 6 X
2 5 5 OK
3 3 6 X
3 4 5 OK
4 4 4 OK