Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the 3rd side.
A) 6cm
B) 5cm
C) 10cm
D) 8cm
Let's use the triangle inequality theorem to determine which choice cannot be the measure of the third side. 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.
For the given triangle, the two sides given measure 4 cm and 9 cm. Let's check each of the choices:
A) 6 cm
The sum of the two given sides is 4 cm + 9 cm = 13 cm. Since 13 cm is greater than 6 cm, this choice could be the measure of the third side.
B) 5 cm
The sum of the two given sides is 4 cm + 9 cm = 13 cm. Since 13 cm is greater than 5 cm, this choice could be the measure of the third side.
C) 10 cm
The sum of the two given sides is 4 cm + 9 cm = 13 cm. Since 13 cm is greater than 10 cm, this choice could be the measure of the third side.
D) 8 cm
The sum of the two given sides is 4 cm + 9 cm = 13 cm. Since 13 cm is not greater than 8 cm, this choice cannot be the measure of the third side.
Therefore, the measure that cannot be the length of the third side is 8 cm.
The correct answer is D) 8 cm.