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
To determine which of the following choices cannot be the measure of the third side of the triangle, we need to use the triangle inequality theorem.
According to the triangle inequality 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 check each choice:
a) 6 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
b) 5 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is greater than 5 cm. Therefore, 5 cm can be the measure of the third side.
c) 13 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is equal to 13 cm. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side (not equal to). Therefore, 13 cm cannot be the measure of the third side.
d) 15 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is less than 15 cm. Therefore, 15 cm can be the measure of the third side.
Therefore, the third side cannot measure 13 cm. So, the correct answer is c) 13 cm.
I only have options: A(5, B(6, C(10, and D(8
Apologies for the confusion.
Let me re-evaluate the options using the triangle inequality theorem:
a) 5 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is greater than 5 cm. Therefore, 5 cm can be the measure of the third side.
b) 6 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
c) 10 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is less than 10 cm. Therefore, 10 cm cannot be the measure of the third side.
d) 8 cm
The sum of the lengths of the two given sides is 4 cm + 9 cm = 13 cm, which is less than 8 cm. Therefore, 8 cm cannot be the measure of the third side.
Therefore, the third side cannot measure 10 cm or 8 cm. So, the correct answer is c) 10 cm.