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:

To determine if a set of three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. We will check each option:

Step 1: Check Option 1 (2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.)

• For 2, 4, 6: $2 + 4 = 6$, which is not greater than 6. So, this set does not form a triangle.

Step 2: Check Option 2 (2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.)

• For 3, 4, 7: $3 + 4 = 7$, which is not greater than 7. So, this set does not form a triangle.

Step 3: Check Option 3 (2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.)

• For 2, 3, 4:
• $2 + 3 = 5 > 4$
• $2 + 4 = 6 > 3$
• $3 + 4 = 7 > 2$
• For 5, 6, 7:
• $5 + 6 = 11 > 7$
• $5 + 7 = 12 > 6$
• $6 + 7 = 13 > 5$

Both sets satisfy the triangle inequality theorem.

Step 4: Check Option 4 (2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.)

• For 2, 3, 6: $2 + 3 = 5 < 6$. So, this set does not form a triangle.

Answer:

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