Can you make a triangle with these three objects? Use the Triangle Inequality Theorem to explain why or why not.
1. Measurements of the three objects you picked: 3 inches, 6 inches, and 4 inches
2. Use the Triangle Inequality Theorem to explain why or why not you can form a triangle!! Show the math!
To determine if a triangle can be formed using the three objects with measurements of 3 inches, 6 inches, and 4 inches, we need to apply the Triangle Inequality Theorem.
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 condition is satisfied for the three objects:
Condition 1: Sum of length of two sides > Length of remaining side
1. Side with length 3 inches + Side with length 6 inches > Side with length 4 inches
3 + 6 > 4
9 > 4
The condition is satisfied.
Condition 2: Sum of length of two sides > Length of remaining side
2. Side with length 3 inches + Side with length 4 inches > Side with length 6 inches
3 + 4 > 6
7 > 6
The condition is also satisfied.
Condition 3: Sum of length of two sides > Length of remaining side
3. Side with length 6 inches + Side with length 4 inches > Side with length 3 inches
6 + 4 > 3
10 > 3
Again, the condition is satisfied.
Since all three conditions are met, we can conclude that a triangle can be formed using the three objects with measurements of 3 inches, 6 inches, and 4 inches.