ANYONE GOOD AT GEOMETRY

i forgot how to do this certain topic:
identifying triangles. help me with this open response?

marrisa has 4 metal rods of different lengths as shown below. Her math assignment requires her to make different size triangles using only these rods. She will choose 3 of the 4 rods and place them together to see if they form a triangle. She will record the rod lengths used and identify if a triangle was formed. She will repeat the process until she has used all combinations of rod lengths.

rod lengths:

6 cm
8 cm
12 cm
21 cm

QUESTIONS:

1. Identify all of the different size triangles that can be formed using the given rods. Show or explain all work.
2. Would any of the triangles identified in part 1 form right triangless? Show or explain all work.

1. To design a triangle, the longest side (hypotenuse) must not equal or exceed the sum of the other two lengths. That is, if you have lengths 3cm and 4cm, the third length must be between 1cm and 7cm.

So let's take a look at the possible combinations of lengths.
6cm, 8cm, 12cm. This one works, because 12cm is less than 14 cm. (6+8)
6cm, 8cm, 21cm. This does not work because 21cm is greater than 14 cm.
6cm, 12cm, 21cm. This does not work because 21cm is greater than 18 cm. (6 + 12)
8cm, 12cm, 21cm. This does not work, because 21cm is longer than 20cm. (8+12)

So the only combination that works is the first one. (6cm, 8cm, 12cm).

2. Since there was only one possibility, we can try this out using the Pythagorean theorem.

See if this is true: 6^2 + 8^2 = 12^2

6^2 = 36
8^2 = 64
12^2 = 144

But, 36 + 64 does not equal 144. There are no possible right triangles.

Here are the four distinct choices or rods:
#1...#2....#3...Short 1 + Short 2...Max
6......8....12.....6+8 = 14..........12
6......8....21.....6+8=14............21
6.....12...21.....6+12=18.........21