Final answer:
The set of side lengths that will make a triangle is: B) 18cm, 24cm, 40cm.
Step-by-step explanation:
A triangle is a polygon with three sides. To determine if a set of side lengths can form a triangle, we use 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.
Let's apply this theorem to the given options:
A. 16cm, 22cm, 40cm: 16 + 22 = 38 < 40. This does not satisfy the triangle inequality, so it is not a triangle.
B. 18cm, 24cm, 40cm: 18 + 24 = 42 > 40. This satisfies the triangle inequality, so it is a triangle.
C. 16cm, 24cm, 40cm: 16 + 24 = 40 > 40. This satisfies the triangle inequality, so it is a triangle.
D. 18cm, 20cm, 40cm: 18 + 20 = 38 < 40. This does not satisfy the triangle inequality, so it is not a triangle.
Therefore, the correct answer is B. 18cm, 24cm, 40cm.