Answer:
9 possible combinations: RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP
Step-by-step explanation:
- <em>
We need to consider The Triangle Inequality Theorem which states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
</em>
<u>Let's see what are the possible combinations:
</u>
3+4= 7 so possible 3rd side is 5
3+5= 8 so possible 3 rd side is 7
3+7= 10 so possible 3rd side is 5 or 9 (5 is repeat of the one above)
3+9= 12 so possible 3rd side is 7, see one above
3+12= 15 so possible 3 rd side is none
4+5=9 so possible 3rd side is 7
4+7= 11 so possible 3rd side is 9
4+9= 13 so possible 3rd side is 12
5+7= 12 so possible 3rd side is 9
5+9= 14 so possible 3rd side is 12
7+9= 16 so possible 3rd side is 12
So the possible 9 combinations are:
RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP
