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
8 cm
8 cm
10 cm
10 cm
5 cm
5 cm
6 cm
To determine which choice cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem. This 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 to see if it satisfies the triangle inequality theorem:
1. 8 cm: 4 + 8 = 12 (greater than 9), 9 + 8 = 17 (greater than 4), this choice satisfies the theorem.
2. 8 cm: Same as the first choice, it satisfies the theorem.
3. 10 cm: 4 + 10 = 14 (greater than 9), 9 + 10 = 19 (greater than 4), this choice satisfies the theorem.
4. 10 cm: Same as the third choice, it satisfies the theorem.
5. 5 cm: 4 + 5 = 9 (equal to 9), this choice does not satisfy the theorem.
6. 5 cm: Same as the fifth choice, it does not satisfy the theorem.
7. 6 cm: 4 + 6 = 10 (greater than 9), 9 + 6 = 15 (greater than 4), this choice satisfies the theorem.
Based on the triangle inequality theorem, the measurements that cannot be the measure of the third side of the triangle are:
5 cm and 5 cm.
So, the correct answer is:
5 cm
5 cm