Question

Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side.

A) 5.5
B) 4.5
C) 3.5
D) 4.2

Answer 1

there is one answer

Answer 2

To apply the Triangle Inequality Theorem, we need to know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, let's consider the two given sides: 3.7 and 8.2.

For the Triangle Inequality Theorem to hold true, the sum of these two sides must be greater than the length of the third side.

So we have:

3.7 + 8.2 > third side length

11.9 > third side length

Therefore, a possible measure of the third side could be any value greater than 11.9.

None of the answer choices (A) 5.5, (B) 4.5, (C) 3.5, or (D) 4.2 are greater than 11.9.

Thus, none of the answer choices are possible measures for the third side.

Answer 3

I apologize for my mistake. Let's reconsider the options using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the two sides of the triangle measure 3.7 and 8.2, we can write the following inequality:

3.7 + 8.2 > third side length

11.9 > third side length

From the given answer choices, the only option that is greater than 11.9 is (A) 5.5.

Therefore, the possible measure of the third side is 5.5.

The correct answer is A) 5.5.