Question

Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.(1 point)

Answer 1

To determine if the sides with lengths 4 inches, 8 inches, and 9 inches form a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the remaining side.

Based on the Triangle Inequality Theorem, for any triangle with sides a, b, and c, the following inequality must hold:

a + b > c
b + c > a
a + c > b

Let's check if these conditions are true for the given sides:

4 + 8 > 9 --> 12 > 9 (True)
8 + 9 > 4 --> 17 > 4 (True)
4 + 9 > 8 --> 13 > 8 (True)

The conditions hold true for all pairs of sides, therefore, the sides with lengths 4 inches, 8 inches, and 9 inches form a triangle.