Question

Two sides of a triangle measure 4 cm and 9 cm determine which of the following choices can not be the measure of the third side answer choices 10cm,5cm,8cm,6cm

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine which of the given choices can not be the measure of the third side of the triangle, we can apply 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.

Let the two given sides be 4 cm and 9 cm.
Therefore, the third side must satisfy the following conditions:
- 4 + 9 > Third side
- 9 + Third side > 4
- 4 + Third side > 9

Let's calculate:
- 4 + 9 = 13
- 9 + 4 = 13
- 4 + 9 = 13

Comparing these conditions with the given choices:
- 10cm: 13 > 10 (valid)
- 5cm: 13 > 5 (valid)
- 8cm: 13 > 8 (valid)
- 6cm: 13 = 6 (invalid)

Therefore, the third side cannot be 6cm.