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Can you construct a triangle with sides 7 cm, 3 cm, 12 cm? Why or Why not?

User Sam Benson
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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

User Jtyler
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