Question

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, this triangle is not possible

Explanation:

By the Triangle Inequality Theorem, it should be that:

a + b > c,

a + c > b, ⇒ a, b, and c are sides of this triangle

b + c > a

~ In this case let us say a = 4 inches, b = 6 inches, and c = 11 inches ~

4 + 6 > 11,

4 + 11 > 6, ⇒ Here 10 is not greater than 3rd side and thus

11 + 6 > 4 doesn't form a triangle

Answer 2

No, because side 11 is greater than the sum of the two other sides.