Final answer:
A triangle with sides measuring 7 cm, 3 cm, and 12 cm cannot be constructed. The sum of the lengths of two shorter sides (7 cm and 3 cm) is not greater than the length of the longest side (12 cm), violating the Triangle Inequality Theorem.
Step-by-step explanation:
The question is asking whether it's possible to construct a triangle with sides 7 cm, 3 cm, and 12 cm. In Geometry, we have something known as 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.
In this case, if we add the lengths of the two smaller sides, 7 cm + 3 cm = 10 cm, we see that this is not greater than the length of the largest side, 12 cm.
Therefore, it is not possible to construct a triangle with sides 7 cm, 3 cm, and 12 cm due to the Triangle Inequality Theorem.
Learn more about Triangle Inequality Theorem