11. If a triangle has lengths of 27 m and 11 m , check all the possible lengths for the third side. a 39 m 17 m 35 m a 16 m a

To determine the possible lengths for the third side of a triangle, you can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the third side. In your case, if one side is 27 m and another is 11 m, the third side (let's call it "x") must satisfy two conditions: \(27 + 11 > x\), and \(27 - 11 < x\). This gives us the range \(16 < x < 38\). Therefore, the only valid options for the third side are 17 m and 35 m. Always remember to double-check the lengths you consider! One common error is mistakenly thinking a value is possible when it doesn't meet the triangle inequality theorem's criteria. To have a triangle, just keep in mind that you must be able to form a closed shape with your side lengths—if they don’t work together, it’s time to rethink your options!