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------------------------------------------------ The side lengths of a triangle are 43.1, 13.1, and 55.2. Which of the following is true?

A. The side lengths shown are possible because the longest length must be less than 56.2 inches, but greater than 30.

B. The side lengths shown are possible because the shortest side must be greater than 98.3 inches.

C. The side lengths shown are not possible because the longest length must be greater than 56.2 inches.

D. The side lengths shown are not possible because the shortest side must be 12.1 inches, but greater than 4.1 inches.

The given side lengths of 43.1, 13.1, and 55.2 inches satisfy the triangle inequality theorem, so they are possible for a triangle, making option A the correct answer.

Explanation:

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Applying this theorem to the given side lengths of 43.1, 13.1, and 55.2 inches, we can analyze the given options.

To determine if these side lengths can form a triangle, we need to check two sums: 43.1 + 13.1 (which equals 56.2) must be greater than 55.2, and 43.1 + 55.2 (which equals 98.3) must be greater than 13.1. Both conditions are satisfied.

Since the longest side (55.2 inches) is less than the sum of the other two sides, and each sum of two sides is greater than the third side, the given side lengths are possible for a triangle. Therefore, the correct answer is option A: The side lengths shown are possible because the longest length must be less than 56.2 inches, but greater than 30.