Final answer:
To determine which sets of two sides are possible for the lengths of the other two sides of the triangle, we can use the triangle inequality theorem. Sets A (5 cm and 8 cm), B (6 cm and 7 cm), and D (8 cm and 9 cm) are possible.
Step-by-step explanation:
To determine which set of two sides is possible for the lengths of the other two sides of the triangle, we can use 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 third side.
Let's examine each set of sides:
- Set A: 5 cm and 8 cm. 5 + 8 = 13, which is equal to the known side length of 13 cm. This set is possible.
- Set B: 6 cm and 7 cm. 6 + 7 = 13, which is equal to the known side length of 13 cm. This set is possible.
- Set C: 7 cm and 2 cm. 7 + 2 = 9, which is less than the known side length of 13 cm. This set is not possible.
- Set D: 8 cm and 9 cm. 8 + 9 = 17, which is greater than the known side length of 13 cm. This set is possible.
Therefore, the possible sets of two sides for the triangle are Set A (5 cm and 8 cm), Set B (6 cm and 7 cm), and Set D (8 cm and 9 cm).