It's not possible to build a triangle with side lengths of 3, 3, and 9.
A. True
B. False
Answer (2)
Apply the triangle inequality theorem to check if the sum of any two sides is greater than the third side.
Check the inequalities: 9"> 3 + 3 > 9 , 3"> 3 + 9 > 3 , and 3"> 3 + 9 > 3 .
Since 3 + 3 = 6 which is not greater than 9, the triangle inequality is not satisfied.
Conclude that it is not possible to build a triangle with the given side lengths, so the statement is T r u e .
Explanation
Understanding the Triangle Inequality Theorem To determine if it's possible to build a triangle with side lengths 3, 3, and 9, we need to apply the triangle inequality theorem. This 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.
Checking the inequalities Let's check the three possible combinations of sides:
3 + 3 > 9
3 + 9 > 3
3 + 9 > 3
Evaluating the inequalities Now, let's evaluate each inequality:
3 + 3 = 6, and 6 > 9 is false.
3 + 9 = 12, and 12 > 3 is true.
3 + 9 = 12, and 12 > 3 is true.
Since the first inequality (3 + 3 > 9) is false, the triangle inequality theorem is not satisfied.
Conclusion Therefore, it is not possible to build a triangle with side lengths 3, 3, and 9. The statement "It's not possible to build a triangle with side lengths of 3, 3, and 9" is true.
Examples
The triangle inequality theorem is useful in various real-world scenarios, such as construction and navigation. For example, when building a bridge, engineers need to ensure that the lengths of the supporting beams satisfy the triangle inequality to ensure the structure's stability. Similarly, in navigation, understanding the triangle inequality helps determine the shortest path between two points, considering the lengths of different routes.
It is not possible to form a triangle with the side lengths of 3, 3, and 9 due to the triangle inequality theorem. The sum of the lengths of two sides (3 + 3) does not exceed the length of the third side (9). Thus, the answer to the question is True.
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