SHOW HOW YOU KNOW if the three lengths can form a triangle. $$ 25,17,29 $$ True False

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UpStudy AI · Accepted Answer

1. To determine if the side lengths $$25$$, $$17$$, and $$29$$ can form a triangle, we need to check the triangle inequality theorem which states that the sum of any two sides must be greater than the remaining side.

2. We check the first inequality:  
   $$
   25 < 17 + 29 \quad \Rightarrow \quad 25 < 46
   $$
   This condition is satisfied.

3. Next, we check the second inequality:  
   $$
   17 < 25 + 29 \quad \Rightarrow \quad 17 < 54
   $$
   This condition is also satisfied.

4. Finally, we check the third inequality:  
   $$
   29 < 25 + 17 \quad \Rightarrow \quad 29 < 42
   $$
   This condition is satisfied as well.

5. Since all three inequalities hold true, the lengths $$25$$, $$17$$, and $$29$$ can indeed form a triangle.

Final Answer: True
The lengths 25, 17, and 29 can form a triangle because the sum of any two lengths is greater than the third length.

SHOW HOW YOU KNOW if the three lengths can form a triangle. \[ 25,17,29 \] True False

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