Final answer:
Using the triangle inequality theorem, the minimum side length to complete a triangle with sides of 28cm and 21cm is slightly greater than 7cm, and the maximum side length is slightly less than 49cm.
Step-by-step explanation:
To determine the minimum and maximum lengths to complete a triangle with two side lengths of 28cm and 21cm, we use the triangle inequality theorem. This theorem states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Minimum Length:
To find the minimum side length, we subtract the length of the smaller side from the larger side: 28cm - 21cm = 7cm. To satisfy the triangle inequality theorem, we must add a small value (which can be as small as we like, for example, 0.01cm) to this difference. Thus, the minimum length is slightly greater than 7cm.
Maximum Length:
To find the maximum side length, we add both side lengths together: 28cm + 21cm = 49cm. The maximum length must be less than this sum for the triangle inequality theorem to hold. Therefore, the maximum length is slightly less than 49cm.