Problem

11. Determine if it is possible to form a triangle with the given side lengths:
$41 \mathrm{in}, 12 \mathrm{in}, 20 \mathrm{in}$
O Possible
Not possible

Answer

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Answer

So, the final answer is \(\boxed{\text{Not possible}}\).

Steps

Step 1 :The sum of any two sides of a triangle must be bigger than the third side.

Step 2 :If the sides were $41$ in, $12$ in, and $20$ in, we need to check if the sum of any two sides is greater than the third side.

Step 3 :For sides $41$ in and $12$ in, their sum is $41+12=53$ in, which is greater than the third side $20$ in.

Step 4 :For sides $41$ in and $20$ in, their sum is $41+20=61$ in, which is greater than the third side $12$ in.

Step 5 :For sides $12$ in and $20$ in, their sum is $12+20=32$ in, which is less than the third side $41$ in.

Step 6 :Since the sum of the lengths of the two shorter sides $12$ in and $20$ in is not greater than the length of the longest side $41$ in, it is not possible to form a triangle with these side lengths.

Step 7 :So, the final answer is \(\boxed{\text{Not possible}}\).

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