Question

Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?

2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.
2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.

Answer 1

C: 2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.

Answer 2

1.

3 numbers a, b and c can be the side lengths of a triangle only if all of these hold:
i) a+b>c
ii) a+c>b
iii) b+c>a
This is called "the triangle inequality"

2. Consider the 4 cases separately

Case 1

2+4 is not > 6 so not possible

Case 2

3+4 not > 7 so not possible

Case 3
2+3>4
3+4>2
2+4>3

5+6>7
6+7>5
5+7>6

So possible

Case 4

2+3 not > 6, so not possible