2 sides of a triangle measure 4cm and 9cm determine which of the following choices cannot be the measure of the third side.
The options are
6cm
8cm
5cm
10cm
To determine which of the following choices cannot be the measure of the third side, we need to use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's evaluate the options:
1) If the two sides of a triangle measure 4 cm and 9 cm, the sum of these sides is 4 cm + 9 cm = 13 cm. To fulfill the triangle inequality theorem, the length of the third side must be greater than (but not equal to) 13 - 4 = 9 cm and less than 13 + 4 = 17 cm:
- A third side of 6 cm fulfills the inequality (9 < 6 < 13 + 4), so it can be the measure of the third side.
- A third side of 8 cm also fulfills the inequality (9 < 8 < 13 + 4), so it can be the measure of the third side.
- A third side of 5 cm does not satisfy the inequality (9 < 5), so it cannot be the measure of the third side.
- A third side of 10 cm fulfills the inequality (9 < 10 < 13 + 4), so it can be the measure of the third side.
Therefore, the answer is that 5 cm cannot be the measure of the third side.