Apply the Triangle Inequality Theorem to determine whether sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.(1 point)
To determine if the sides with lengths 4 inches, 8 inches, and 9 inches form a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the remaining side.
Based on the Triangle Inequality Theorem, for any triangle with sides a, b, and c, the following inequality must hold:
a + b > c
b + c > a
a + c > b
Let's check if these conditions are true for the given sides:
4 + 8 > 9 --> 12 > 9 (True)
8 + 9 > 4 --> 17 > 4 (True)
4 + 9 > 8 --> 13 > 8 (True)
The conditions hold true for all pairs of sides, therefore, the sides with lengths 4 inches, 8 inches, and 9 inches form a triangle.
To apply the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
Let's take the sides with lengths 4 inches, 8 inches, and 9 inches:
- Side 1: 4 inches
- Side 2: 8 inches
- Side 3: 9 inches
Now, we check if the sum of any two sides is greater than the length of the remaining side:
- Side 1 + Side 2 = 4 inches + 8 inches = 12 inches
- Since 12 inches is greater than Side 3 (9 inches), the inequality holds.
- Side 1 + Side 3 = 4 inches + 9 inches = 13 inches
- Again, 13 inches is greater than Side 2 (8 inches), so the inequality holds.
- Side 2 + Side 3 = 8 inches + 9 inches = 17 inches
- Once more, 17 inches is greater than Side 1 (4 inches), so the inequality holds.
Since the sum of any two sides is greater than the length of the remaining side in all three cases, we can conclude that the sides with lengths 4 inches, 8 inches, and 9 inches do form a triangle.
To apply the Triangle Inequality Theorem, you need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side. Let's determine if the sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle:
Step 1: Arrange the side lengths in increasing order: 4 inches, 8 inches, 9 inches.
Step 2: Take the two smallest side lengths (4 inches and 8 inches) and add them together: 4 + 8 = 12 inches.
Step 3: Compare the sum obtained in the previous step with the length of the remaining side (9 inches).
If the sum of the two smallest side lengths is greater than the length of the remaining side, then the given lengths form a triangle. Otherwise, they do not.
In this case, since 12 inches is greater than 9 inches, the sum of the two smallest side lengths is greater than the length of the remaining side, and therefore, the sides with lengths of 4 inches, 8 inches, and 9 inches form a triangle.