Question

Determine whether you can construct many, one, or no triangle(s) wit

the given description. Explain your reasoning.
7. a triangle with a 2-inch side, a 4-inch side, and a 5-inch side

Answer 1

You can construct one triangle with a 2-inch side, a 4-inch side, and a 5-inch side.

This is because of 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, the 2-inch side is less than the sum of the 4-inch and 5-inch sides, and the 4-inch side is less than the sum of the 2-inch and 5-inch sides, so the conditions of the triangle inequality theorem are satisfied. Therefore, it is possible to form a triangle with these side lengths.