SHOW HOW YOU KNOW if the three lengths can form a triangle. \[ 16,6,2 \] True False
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To determine if the lengths 16, 6, and 2 can form a triangle, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Let's check: 1. 16 + 6 > 2 (True) 2. 16 + 2 > 6 (True) 3. 6 + 2 > 16 (False) Since the last condition is false, these lengths cannot form a triangle. Therefore, the answer is False! To spice things up, think of triangles as the building blocks of geometry! They can showcase everything from stress distribution in bridges to the coolest design in architecture. Understanding triangle properties can help you grasp the concepts of balance and strength in structures all around us. So, the next time you're gazing at a building, remember the trusty triangles that hold it all together!
