To determine the range of possible lengths [tex]\( x \)[/tex] for the third side of the A-frame restaurant, we can use the triangle inequality theorem.
1. According to the triangle inequality theorem, the length of one side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.
2. Let's denote the two given side lengths as 20 meters and 30 meters.
3. The length of the third side [tex]\( x \)[/tex] must be:
- Greater than the absolute difference of the given sides: [tex]\( |20 - 30| = 10 \)[/tex]
- Less than the sum of the given sides: [tex]\( 20 + 30 = 50 \)[/tex]
Therefore, the inequality describing the range of possible lengths [tex]\( x \)[/tex] of the third side is:
[tex]\[ 10 < x < 50 \][/tex]
So, the completed inequality is:
[tex]\[ 10 < x < 50 \][/tex]
