Question

Explaining the Possibility of a Triangle
Gerry wants to construct a triangle with segments that are 4, 6, and 11 inches long. Is his triangle possible? Explain how you know.

Answer 1

No. By the triangle inequality, the sum of any two side lengths must be greater than the third. Here 4 + 6 = 10, which is less than 11, so the two shorter segments cannot reach the ends of the longest segment. Therefore a triangle with side lengths 4, 6, and 11 is impossible.