Question

Wayne's deli sells whole sandwiches and half sandwiches. The half sandwiches are in the shape of a triangle because they are cut diagonally. Wayne needs to order triangular-shaped containers for the half sandwiches, but he cannot find the file on his laptop that has the measurements. Wayne believes the side lengths of the containers are 9 inches, 3 inches, and 5 inches. Could those be the correct measurements?

Answer 1

The proposed side lengths of 9 inches, 3 inches, and 5 inches do not satisfy the triangle inequality theorem and thus cannot form a triangle. Wayne needs to find the correct measurements to order suitable containers for his deli's half sandwiches.

Step-by-step explanation:

The question pertains to whether the side lengths of 9 inches, 3 inches, and 5 inches could form a triangle. In the context of triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side for a triangle to exist. Therefore, to determine the validity of the side lengths for Wayne's deli sandwich containers, the inequality must be checked for all combinations of the three sides.

Let's test each combination:

• 9 + 3 > 5
• 9 + 5 > 3
• 3 + 5 > 9

Clearly, the third condition, 3 + 5 > 9, is not true because 8 is not greater than 9. Thus, according to the triangle inequality theorem, side lengths of 9 inches, 3 inches, and 5 inches cannot form a triangle. Wayne would need to reassess the measurements for ordering correct triangular-shaped containers.