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?