To determine if a triangle can be formed with sides measuring 14 cm, 8 cm, and 5 cm, we need to check the Triangle Inequality Theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Now, let’s apply the theorem to our side lengths:
- First, we add the lengths of the two shorter sides: 8 cm + 5 cm = 13 cm. This must be greater than the longest side, which is 14 cm. Since 13 cm < 14 cm, the first condition fails.
- Next, let’s check the second condition by adding the longest side (14 cm) and one of the shorter sides (8 cm): 14 cm + 8 cm = 22 cm. This is greater than the other side 5 cm, so this condition holds.
- Finally, add the other shorter side (5 cm) to the longest side (14 cm): 14 cm + 5 cm = 19 cm. This is greater than 8 cm, so this condition holds as well.
Although the last two conditions hold true, since the first condition does not, we conclude that it is not possible to construct a triangle with the given sides. Hence, the answer is: