To determine which of the given choices cannot be the measure of the third side, we can use the triangle inequality theorem. 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 with side lengths measuring 4 cm and 9 cm, the third side must be less than the sum of these two sides, but greater than the difference between these two sides.
The sum of 4 cm and 9 cm is 13 cm, so the third side must be less than 13 cm.
The difference between 9 cm and 4 cm is 5 cm, so the third side must be greater than 5 cm.
Now, we can check each of the given choices to determine which one does not satisfy these conditions:
1) 5 cm:
5 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
2) 8 cm:
8 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
3) 10 cm:
10 cm is greater than 5 cm and greater than 13 cm. It does not satisfy the conditions and cannot be the measure of the third side.
4) 6 cm:
6 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
Therefore, the measure of the third side that cannot be selected is 10 cm.
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
5 cm
5 cm
8 cm
8 cm
10 cm
10 cm
6 cm
3 answers
wrong
I apologize for the mistake in my previous response. Let's reassess the problem.
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.
For the given triangle with side lengths measuring 4 cm and 9 cm, we can determine the possible range for the third side:
The third side must be greater than the difference between the two known side lengths: 9 cm - 4 cm = 5 cm.
The third side must be less than the sum of the two known side lengths: 9 cm + 4 cm = 13 cm.
Now let's check the given choices:
1) 5 cm:
5 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
2) 8 cm:
8 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
3) 10 cm:
10 cm is greater than 5 cm, but it exceeds the upper limit of 13 cm. Therefore, 10 cm cannot be the measure of the third side.
4) 6 cm:
6 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
Therefore, the measure of the third side that cannot be selected is 10 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.
For the given triangle with side lengths measuring 4 cm and 9 cm, we can determine the possible range for the third side:
The third side must be greater than the difference between the two known side lengths: 9 cm - 4 cm = 5 cm.
The third side must be less than the sum of the two known side lengths: 9 cm + 4 cm = 13 cm.
Now let's check the given choices:
1) 5 cm:
5 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
2) 8 cm:
8 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
3) 10 cm:
10 cm is greater than 5 cm, but it exceeds the upper limit of 13 cm. Therefore, 10 cm cannot be the measure of the third side.
4) 6 cm:
6 cm is greater than 5 cm and less than 13 cm. It satisfies the conditions and can be the measure of the third side.
Therefore, the measure of the third side that cannot be selected is 10 cm.