Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches form a triangle.
To determine if a triangle can be formed with these side lengths, we need to check if the sum of the lengths of any two sides is always greater than the length of the third side.
Let's check the first condition: 4.24 + 9.89 > 8.75
This becomes 14.13 > 8.75, which is true.
Now let's check the second condition: 4.24 + 8.75 > 9.89
This becomes 12.99 > 9.89, which is true.
Finally, let's check the third condition: 9.89 + 8.75 > 4.24
This becomes 18.64 > 4.24, which is true.
Since all three conditions are true, we can conclude that sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches can form a triangle.
Apply the Triangle Inequality Theorem to determine whether a triangle can be formed from sides of lengths 7 millimeters, 8 millimeters, and 9 millimeters.
To determine if a triangle can be formed with these side lengths, we need to check if the sum of the lengths of any two sides is always greater than the length of the third side.
Let's check the first condition: 7 + 8 > 9
This becomes 15 > 9, which is true.
Now let's check the second condition: 7 + 9 > 8
This becomes 16 > 8, which is true.
Finally, let's check the third condition: 8 + 9 > 7
This becomes 17 > 7, which is true.
Since all three conditions are true, we can conclude that sides with lengths of 7 millimeters, 8 millimeters, and 9 millimeters can form a triangle.
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 5 inches, 10 inches, and 15 inches form a triangle.
To determine if a triangle can be formed with these side lengths, we need to check if the sum of the lengths of any two sides is always greater than the length of the third side.
Let's check the first condition: 5 + 10 > 15
This becomes 15 > 15, which is false.
Since the first condition is false, we can conclude that sides with lengths of 5 inches, 10 inches, and 15 inches cannot form a triangle based on the Triangle Inequality Theorem.
Apply the Triangle Inequality Theorem to determine whether sides with lengths of 3 inches, 4 inches, and 9 inches form a triangle.
To determine if a triangle can be formed with these side lengths, we need to check if the sum of the lengths of any two sides is always greater than the length of the third side.
Let's check the first condition: 3 + 4 > 9
This becomes 7 > 9, which is false.
Since the first condition is false, we can conclude that sides with lengths of 3 inches, 4 inches, and 9 inches cannot form a triangle based on the Triangle Inequality Theorem.