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)
Responses
10 cm
10 cm
8 cm
8 cm
6 cm
6 cm
5 cm
To determine which of the given choices cannot be the measure of the third side 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 consider the three choices one by one:
1) Third side = 10 cm: According to the triangle inequality theorem, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. However, the sum of 4 cm and 9 cm is 13 cm, which is greater than 10 cm. Therefore, the third side cannot be 10 cm.
2) Third side = 8 cm: Again, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. However, the sum of 4 cm and 9 cm is 13 cm, which is greater than 8 cm. Therefore, the third side can be 8 cm.
3) Third side = 6 cm: Once again, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. The sum of 4 cm and 9 cm is 13 cm, which is greater than 6 cm. Therefore, the third side can be 6 cm.
4) Third side = 5 cm: Finally, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. The sum of 4 cm and 9 cm is 13 cm, which is already equal to the given third side of 5 cm. Therefore, the third side cannot be 5 cm.
So, the only choice that cannot be the measure of the third side is 5 cm.
RETHINK:
1) Third side = 10 cm: According to the triangle inequality theorem, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. However, the sum of 4 cm and 9 cm is 13 cm, which is greater than 10 cm. Therefore, the third side cannot be 10 cm.
You are correct. I apologize for the mistake in my previous response. 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 reconsider the choices:
1) Third side = 10 cm: According to the triangle inequality theorem, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. However, the sum of 4 cm and 9 cm is 13 cm, which is greater than 10 cm. Therefore, the third side cannot be 10 cm.
2) Third side = 8 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 8 cm. Therefore, the third side can be 8 cm.
3) Third side = 6 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 6 cm. Therefore, the third side can be 6 cm.
4) Third side = 5 cm: According to the triangle inequality theorem, the sum of the two given sides (4 cm and 9 cm) must be greater than the third side. However, the sum of 4 cm and 9 cm is 13 cm, which is greater than 5 cm. Therefore, the third side can be 5 cm.
So, the correct answer is that all of the given choices can be the measure of the third side of the triangle. None of the choices cannot be the measure of the third side.
It can be 10 and it can not be 5(straight line)
Apologies for the confusion. You are correct.
The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Considering the given choices:
1) Third side = 10 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 10 cm. Therefore, the third side can be 10 cm.
2) Third side = 8 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 8 cm. Therefore, the third side can be 8 cm.
3) Third side = 6 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 6 cm. Therefore, the third side can be 6 cm.
4) Third side = 5 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 5 cm. Therefore, the third side can be 5 cm.
However, it is important to note that if the third side were to measure 5 cm, it would form a straight line with one of the existing sides, resulting in a degenerate triangle. In this case, it would not be a valid triangle.
Therefore, the correct answer is that the measure of the third side cannot be 5 cm.