Apply the triangle inequality theorem to determine whether sides with lengths of 4 inches 8 inches and 9 inches from a triangle
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check if this is true for the lengths of 4 inches, 8 inches, and 9 inches:
1. The sum of the lengths of the first two sides (4 inches and 8 inches) is 4 + 8 = 12 inches. This sum is greater than the length of the third side (9 inches).
2. The sum of the lengths of the second and third sides (8 inches and 9 inches) is 8 + 9 = 17 inches. This sum is greater than the length of the first side (4 inches).
3. The sum of the lengths of the first and third sides (4 inches and 9 inches) is 4 + 9 = 13 inches. This sum is greater than the length of the second side (8 inches).
Based on these observations, we can conclude that the lengths of 4 inches, 8 inches, and 9 inches can form a triangle.