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.
8 cm
5 cm
10 cm
6 cm
To determine which of the choices cannot be the measure of the third side, we can use the triangle inequality theorem.
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 side lengths of 4 cm and 9 cm:
- 4 + 9 = 13
- 9 + 4 = 13
So, the possible range of the third side length is from 5 to 13 cm.
Now, let's check each of the choices based on the triangle inequality theorem:
1. 8 cm: 4 + 8 = 12 and 8 + 4 = 12, so 8 cm could be the third side.
2. 5 cm: 4 + 5 = 9, so 5 cm could be the third side.
3. 10 cm: 4 + 10 = 14 and 10 + 4 = 14, so 10 cm could be the third side.
4. 6 cm: 4 + 6 = 10 and 6 + 9 = 15, so 6 cm could not be the third side (violates the triangle inequality theorem).
Therefore, out of the given choices, the third side measure of 6 cm cannot be the measure of the third side.
what bout five?
Apologies for the oversight. Let's check for the measure of 5 cm for the third side using the triangle inequality theorem.
Given side lengths of 4 cm and 9 cm:
- 4 + 5 = 9
- 5 + 4 = 9
Based on the calculations above, the measure of the third side can be 5 cm as it satisfies the triangle inequality theorem.
Therefore, out of the given choices, the third side measures of 8 cm, 10 cm, and 6 cm are possible, while 5 cm is also a possible measure of the third side of the triangle.
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.
8 cm
5 cm
10 cm
6 cm
use logic and evauluate twice.
Let's reevaluate the choices by first applying the Triangle Inequality Theorem and then cross-checking to ensure accuracy.
Given side lengths of 4 cm and 9 cm:
- 4 + 9 = 13
- 9 + 4 = 13
Now, we check each choice:
1. 8 cm: 4 + 8 = 12 and 8 + 4 = 12. 8 cm can be the third side.
2. 5 cm: 4 + 5 = 9. 5 cm can be the third side.
3. 10 cm: 4 + 10 = 14 and 10 + 4 = 14. 10 cm can be the third side.
4. 6 cm: 4 + 6 = 10 and 9 + 6 = 15. 6 cm cannot be the third side as it violates the Triangle Inequality Theorem.
Using logic and reevaluation, we determined that 6 cm cannot be the measure of the third side based on the given side lengths of 4 cm and 9 cm.