Final answer:
To determine if a triangle can be formed given three side lengths, apply the triangle inequality theorem by comparing the sum of any two sides to the length of the remaining side. Option B and option D would give triangles.
Step-by-step explanation:
To determine if a triangle can be formed given the measures of three sides, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's examine each given set of side lengths:
A. 2cm, 4cm, 8cm: In this case, 2cm + 4cm = 6cm, which is less than 8cm. So, a triangle cannot be formed with these side lengths.
B. 3cm, 4cm, 6cm: Here, 3cm + 4cm = 7cm, which is greater than 6cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.
C. 4cm, 5cm, 10cm: In this case, 4cm + 5cm = 9cm, which is less than 10cm. So, a triangle cannot be formed with these side lengths.
D. 5cm, 6cm, 12cm: Here, 5cm + 6cm = 11cm, which is greater than 12cm. The sum of any two sides is always greater than the third side, so a triangle can be formed with these side lengths.
Therefore, option B (3cm, 4cm, 6cm) and option D (5cm, 6cm, 12cm) would give triangles.