Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point)
To determine which choice cannot be the measure of the third side, we can use the triangle inequality theorem. According to this theorem, for a triangle with sides measuring a, b, and c, the following inequality holds: a + b > c.
In this case, the given sides of the triangle measure 4 cm and 9 cm. Let's test each choice to see if it satisfies the triangle inequality theorem:
A) 7 cm: 4 cm + 7 cm = 11 cm > 9 cm (satisfied)
B) 13 cm: 4 cm + 13 cm = 17 cm > 9 cm (satisfied)
C) 5 cm: 4 cm + 5 cm = 9 cm (not satisfied)
D) 12 cm: 4 cm + 12 cm = 16 cm > 9 cm (satisfied)
Therefore, the measure of the third side cannot be 5 cm (choice C).