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.

Explanation:

Step1: Check triangle inequality for Option 1

First triangle: $2+4=6$ (not >6, invalid). Second triangle: $3+5>7$, $3+7>5$, $5+7>3$ (valid). Overall invalid.

Step2: Check triangle inequality for Option 2

First triangle: $2+5>6$, $2+6>5$, $5+6>2$ (valid). Second triangle: $3+4=7$ (not >7, invalid). Overall invalid.

Step3: Check triangle inequality for Option 3

First triangle: $2+3>4$, $2+4>3$, $3+4>2$ (valid). Second triangle: $5+6>7$, $5+7>6$, $6+7>5$ (valid). Overall valid.

Step4: Check triangle inequality for Option 4

First triangle: $2+3=5<6$ (invalid). Second triangle: $4+5>7$, $4+7>5$, $5+7>4$ (valid). Overall invalid.

Answer:

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