SHOW HOW YOU KNOW if the three lengths can form a triangle. $$ 16,6,2 $$ True False

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UpStudy AI · Accepted Answer

1. **List the side lengths:**  
   The given side lengths are $$ a = 16 $$, $$ b = 6 $$, and $$ c = 2 $$.

2. **Apply the triangle inequality theorem:**  
   For three sides to form a triangle, the sum of any two sides must be greater than the remaining side. That is:  
   $$
   \begin{aligned}
   a + b &> c, \
   a + c &> b, \
   b + c &> a.
   \end{aligned}
   $$

3. **Check each inequality:**  
   - Check $$ a + b > c $$:  
     $$
     16 + 6 = 22 \quad \text{and} \quad 22 > 2 \quad (\text{True}).
     $$
   - Check $$ a + c > b $$:  
     $$
     16 + 2 = 18 \quad \text{and} \quad 18 > 6 \quad (\text{True}).
     $$
   - Check $$ b + c > a $$:  
     $$
     6 + 2 = 8 \quad \text{and} \quad 8 > 16 \quad (\text{False}).
     $$

4. **Conclusion:**  
   Since the inequality $$ b + c > a $$ is not satisfied, the three lengths cannot form a triangle.

$$
\boxed{\text{False}}
$$
The three lengths 16, 6, and 2 cannot form a triangle because $$ 6 + 2 = 8 $$ is not greater than 16.

SHOW HOW YOU KNOW if the three lengths can form a triangle. \[ 16,6,2 \] True False

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