Final answer:
The lengths 0.9, 4.7, and 6.5 units cannot form a triangle as they violate the Triangle Inequality Theorem since the sum of the smallest two sides is not greater than the third side.
Step-by-step explanation:
To determine whether lengths of 0.9, 4.7, and 6.5 units can form the sides of 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. Considering the given side lengths, let's perform a quick check:
• For sides 0.9 and 4.7, their sum is 5.6, which is less than the third side, 6.5. This violates the Triangle Inequality Theorem and therefore these lengths cannot form a triangle.
This example illustrates why sides with lengths of 0.9, 4.7, and 6.5 cannot be used to construct a triangle. This problem lies within the realm of basic geometry, which is a topic typically covered in high school mathematics classes.
If the lengths were to satisfy the Triangle Inequality Theorem, we could have gone further to categorize the type of triangle (e.g., right, acute, obtuse) by applying the Pythagorean theorem or using angle measurements. Remember, the sum of the angles in any triangle is always 180 degrees.