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
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.
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the two sides of the triangle measure 4 cm and 9 cm.
Let's evaluate the sum of these two sides:
4 cm + 9 cm = 13 cm
Now, let's compare this sum with each of the given choices:
- Choice 1: 8 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 8 cm. Therefore, 8 cm can be the measure of the third side.
- Choice 2: 8 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 8 cm. Therefore, 8 cm can be the measure of the third side.
- Choice 3: 10 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 10 cm. Therefore, 10 cm can be the measure of the third side.
- Choice 4: 10 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 10 cm. Therefore, 10 cm can be the measure of the third side.
- Choice 5: 6 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
- Choice 6: 6 cm
The sum of 4 cm and 9 cm (13 cm) is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
- Choice 7: 5 cm
The sum of 4 cm and 9 cm (13 cm) is not greater than 5 cm. Therefore, 5 cm cannot be the measure of the third side.
Therefore, the choice that cannot be the measure of the third side is 5 cm.