two sides of a triangle measure 4cm and 9cm determain which of the following choises cannot be a measure of the third side
10cm
8cm
5cm
6cm
To determine which of the choices cannot be the measure of the third side of the triangle, we can use 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.
Given that the two sides of the triangle measure 4cm and 9cm:
- 4cm + 9cm > third side
- 13cm > third side
Now, we can test each choice to see if it satisfies the triangle inequality theorem:
1. 10cm: 4cm + 10cm = 14cm > 9cm (satisfied)
2. 8cm: 4cm + 8cm = 12cm > 9cm (satisfied)
3. 5cm: 4cm + 5cm = 9cm = 9cm (not satisfied)
4. 6cm: 4cm + 6cm = 10cm > 9cm (satisfied)
Therefore, the measure of the third side cannot be 5cm, as it does not satisfy the triangle inequality theorem.