Respuesta :
I know this is a bit late but if anyone still needs help with the first question the combinations are ROY, RYG, RGB, OYG, OGB, OBP, YGB, YBP, and GBP.
Answer:
9 possible combinations: RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP
Step-by-step explanation:
- 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.
Let's see what are the possible combinations:
3+4= 7 so possible 3rd side is 5
- 3, 4, 5 or ROY
3+5= 8 so possible 3 rd side is 7
- 3, 5, 7 or RYG
3+7= 10 so possible 3rd side is 5 or 9 (5 is repeat of the one above)
- 3, 7, 9 or RGB
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, 5, 7 or OYG
4+7= 11 so possible 3rd side is 9
- 4, 7, 9 or OGB
4+9= 13 so possible 3rd side is 12
- 4, 9, 12 or OBP
5+7= 12 so possible 3rd side is 9
- 5, 7, 9 or YGB
5+9= 14 so possible 3rd side is 12
- 5, 9, 12 or YBP
7+9= 16 so possible 3rd side is 12
- 7, 9, 12 or GBP
So the possible 9 combinations are:
RGB, RYG, RGB, OYG, OGB, OBP, YGB, YBP, GBP