Final answer:
The measurements 10 cm, 7 cm, and 3 cm do not form a triangle according to the triangle inequality theorem.
Step-by-step explanation:
To determine if the given measurements form a triangle, we utilize the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In our case, we have lengths of 10 cm, 7 cm, and 3 cm. To apply the theorem, we add up every possible pair of these lengths and compare it to the remaining one:
- 10 cm + 7 cm = 17 cm which is greater than 3 cm
- 10 cm + 3 cm = 13 cm which is greater than 7 cm
- 7 cm + 3 cm = 10 cm which is not greater than 10 cm
Since 7 cm + 3 cm is not greater than 10 cm, the measurements do not form a triangle by the triangle inequality theorem.
Learn more about Triangle inequality theorem