The Triangle Inequality Theorem tells us that the sum of the shortest and middle side of a triangle must be greater than the length of the third side. There are two possible scenarios to consider here.
The 10-inch side is the greatest side, which means ML is either the shortest side or the middle side.
The 10-inch side is the middle side, which means ML must be the greatest side.
10-inch Side Is Greatest Side
If the 10-inch side is the greatest, then according to the Triangle Inequality Theorem the sum of 4inches and ML must be greater than 10 inches. We can write this as an inequality.
4+ML > 10 ⇔ ML > 6
ML must be greater than 6 inches.
ML Is Greatest Side
If ML is the greatest side, then the sum of 4 inches and 10 inches must be greater than ML. We can write this as a second inequality.
4+10 > ML ⇔ ML < 14
ML must be less than 14 inches.
Conclusion
Depending on which side is the longest, ML must be between 6 inches and 14 inches.
6inches < ML < 14inches
