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)
• 8 cm
• 6 cm
• 10 cm
• 5 cm
To determine which choice cannot be the measure of the third side, we need to 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 remaining side.
Let's consider each choice:
1) 8 cm: The sum of the two given sides (4 cm + 9 cm) is 13 cm, which is greater than 8 cm. Therefore, 8 cm can be the measure of the third side.
2) 6 cm: The sum of the two given sides (4 cm + 9 cm) is 13 cm, which is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
3) 10 cm: The sum of the two given sides (4 cm + 9 cm) is 13 cm, which is not greater than 10 cm. Therefore, 10 cm cannot be the measure of the third side.
4) 5 cm: The sum of the two given sides (4 cm + 9 cm) is 13 cm, which is greater than 5 cm. Therefore, 5 cm can be the measure of the third side.
So, the measure of the third side that cannot be the length of the third side of the triangle is 10 cm.