Question

Which three lengths could be the lengths of a triangle?

a. 2 cm, 15 cm, 28 cm
b. 14 cm, 6 cm, 20 cm
c. 20 cm, 7 cm, 9 cm
d. 6 cm, 24 cm, 10 cm
e. 10 cm, 15 cm, 24 cm

Answer 1

The sets of lengths that can form triangles, complying with the Triangle Inequality Theorem, are option b (14 cm, 6 cm, 20 cm) and option e (10 cm, 15 cm, 24 cm).

Step-by-step explanation:

The student has asked to identify which sets of three lengths could form a triangle. This can be determined using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

1. 2 cm, 15 cm, 28 cm - This cannot form a triangle because 2 cm + 15 cm is not greater than 28 cm.
2. 14 cm, 6 cm, 20 cm - This can form a triangle because 14 cm + 6 cm is greater than 20 cm, and all the other two-sum combinations are greater than the third side as well.
3. 20 cm, 7 cm, 9 cm - This cannot form a triangle because 7 cm + 9 cm is not greater than 20 cm.
4. 6 cm, 24 cm, 10 cm - This cannot form a triangle because 6 cm + 10 cm is not greater than 24 cm.
5. 10 cm, 15 cm, 24 cm - This can form a triangle because all two-sum combinations are greater than the third side.

Therefore, the sets of lengths that can form triangles are option b (14 cm, 6 cm, 20 cm) and option e (10 cm, 15 cm, 24 cm).