Final answer:
To determine the number of possible triangles, use the triangle inequality theorem. For the given side lengths a = 5cm and b = 7cm, the sum of these sides must be greater than the third side length.
Step-by-step explanation:
To determine the number of possible triangles, we need to use the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's consider side lengths a = 5cm and b = 7cm.
To form a triangle, the sum of these sides (a+b) must be greater than the third side length (c).
So, 5cm + 7cm = 12cm must be greater than c.
Since 12cm is greater than c, there is at least one possible triangle with these side lengths.