For a set of three measurements to be the lengths of the sides of a triangle, the sum of the two shorter sides must be greater than the longest side.
Let's check each set of measurements:
A. 5 inches, 7 inches, 9 inches
The sum of the two shorter sides is 5 + 7 = 12, which is greater than the longest side of 9 inches. Therefore, this set of measurements can be the lengths of the sides of a triangle.
B. 5 inches, 9 inches, 9 inches
The sum of the two shorter sides is 5 + 9 = 14, which is greater than the longest side of 9 inches. Therefore, this set of measurements can be the lengths of the sides of a triangle.
C. 4 inches, 5 inches, 9 inches
The sum of the two shorter sides is 4 + 5 = 9, which is not greater than the longest side of 9 inches. Therefore, this set of measurements cannot be the lengths of the sides of a triangle.
D. 4 inches, 4 inches, 7 inches
The sum of the two shorter sides is 4 + 4 = 8, which is not greater than the longest side of 7 inches. Therefore, this set of measurements cannot be the lengths of the sides of a triangle.
Therefore, the set of measurements that cannot be the lengths of the sides of a triangle is C. 4 inches, 5 inches, 9 inches.