Final answer:
It is not possible to construct a triangle with side lengths of 15, 37, and 53, as they do not satisfy the requirements of the Triangle Inequality Theorem, which requires the sum of any two sides to be greater than the third side.
Step-by-step explanation:
To determine if a triangle can be constructed with side lengths of 15, 37, and 53, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, to check if the lengths given can form a triangle we add the lengths of the two shorter sides and compare the sum to the length of the longest side.
Using the given lengths:
- 15 + 37 = 52
- Since 52 is less than 53, these sides do not satisfy the Triangle Inequality Theorem.
Therefore, it is not possible to construct a triangle with side lengths of 15, 37, and 53 because they do not meet the requirements of the Triangle Inequality Theorem. This theorem is essential when examining possible dimensions for a triangle and plays a critical role in understanding geometric shapes.