Question

PLZ HELP 50 POINTS AND BRAINLIEST!!!!!!!! Karen has a large pile of colored rods. Each color is a different length. She is trying to connect different colored rods to make triangles as part of a hanging sculpture. Here is a list of rod lengths.
Red: 3 inches
Orange: 4 inches
Yellow: 5 inches
Green: 7 inches
Blue: 9 inches
Purple: 12 inches

1. How many triangles can she make with them if each side is a different color? List the combinations that work.



2. Karen was just trying different combinations of colored rods one at a time, placing the colored rods together to see if they make a triangle. What method did you use to determine the triangle options? Which method do you think is better and why?

Answer 1

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