Question
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.
A. 10 cm
B. 8 cm
C. 5 cm
D. 6 cm
A. 10 cm
B. 8 cm
C. 5 cm
D. 6 cm
Answers
Answer
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Answered by
GPT 3.5
To determine which choice cannot be the measure of the third side, we can use the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's test each choice:
A. 10 cm: 4 cm + 9 cm = 13 cm, so 10 cm is less than the sum of the other two sides. This choice cannot be the measure of the third side.
B. 8 cm: 4 cm + 9 cm = 13 cm, so 8 cm is less than the sum of the other two sides. This choice cannot be the measure of the third side.
C. 5 cm: 4 cm + 5 cm = 9 cm, which is equal to the other side. This choice can be the measure of the third side.
D. 6 cm: 4 cm + 6 cm = 10 cm, which is less than the other side. This choice cannot be the measure of the third side.
Therefore, the answer is $\boxed{\text{(A) } 10 \text{ cm}}.$
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's test each choice:
A. 10 cm: 4 cm + 9 cm = 13 cm, so 10 cm is less than the sum of the other two sides. This choice cannot be the measure of the third side.
B. 8 cm: 4 cm + 9 cm = 13 cm, so 8 cm is less than the sum of the other two sides. This choice cannot be the measure of the third side.
C. 5 cm: 4 cm + 5 cm = 9 cm, which is equal to the other side. This choice can be the measure of the third side.
D. 6 cm: 4 cm + 6 cm = 10 cm, which is less than the other side. This choice cannot be the measure of the third side.
Therefore, the answer is $\boxed{\text{(A) } 10 \text{ cm}}.$
Answered by
GPT 3.5
I apologize for the incorrect explanation. Let's re-evaluate the choices.
We have a triangle with sides measuring 4 cm, 9 cm, and an unknown third side.
According to the triangle inequality theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's test each choice:
A. 10 cm: 4 cm + 9 cm = 13 cm, which is greater than 10 cm. So, 10 cm could be the measure of the third side.
B. 8 cm: 4 cm + 9 cm = 13 cm, which is greater than 8 cm. So, 8 cm could be the measure of the third side.
C. 5 cm: 4 cm + 9 cm = 13 cm, which is greater than 5 cm. So, 5 cm could be the measure of the third side.
D. 6 cm: 4 cm + 9 cm = 13 cm, which is greater than 6 cm. So, 6 cm could be the measure of the third side.
Therefore, the answer is None. All of the given choices can be the measure of the third side.
We have a triangle with sides measuring 4 cm, 9 cm, and an unknown third side.
According to the triangle inequality theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's test each choice:
A. 10 cm: 4 cm + 9 cm = 13 cm, which is greater than 10 cm. So, 10 cm could be the measure of the third side.
B. 8 cm: 4 cm + 9 cm = 13 cm, which is greater than 8 cm. So, 8 cm could be the measure of the third side.
C. 5 cm: 4 cm + 9 cm = 13 cm, which is greater than 5 cm. So, 5 cm could be the measure of the third side.
D. 6 cm: 4 cm + 9 cm = 13 cm, which is greater than 6 cm. So, 6 cm could be the measure of the third side.
Therefore, the answer is None. All of the given choices can be the measure of the third side.
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