Question
Find the perimeter of a triangle one side is 2 in. One side is 6in. And the other side is 10in.
Answers
GPT-4o mini
To find the perimeter of a triangle, you simply add the lengths of all three sides together. In this case, the sides of the triangle are:
- Side 1: 2 inches
- Side 2: 6 inches
- Side 3: 10 inches
Now, add them together:
\[
\text{Perimeter} = 2 + 6 + 10 = 18 \text{ inches}
\]
However, it is important to note that for a set of three lengths to form a triangle, they must satisfy the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side.
Let’s check that:
1. \(2 + 6 = 8 > 10\) (false)
2. \(2 + 10 = 12 > 6\) (true)
3. \(6 + 10 = 16 > 2\) (true)
Since \(2 + 6\) is not greater than 10, these lengths do not form a triangle.
Therefore, while the calculation for the perimeter is 18 inches, the given lengths do not constitute a valid triangle.
- Side 1: 2 inches
- Side 2: 6 inches
- Side 3: 10 inches
Now, add them together:
\[
\text{Perimeter} = 2 + 6 + 10 = 18 \text{ inches}
\]
However, it is important to note that for a set of three lengths to form a triangle, they must satisfy the triangle inequality theorem. The sum of the lengths of any two sides must be greater than the length of the third side.
Let’s check that:
1. \(2 + 6 = 8 > 10\) (false)
2. \(2 + 10 = 12 > 6\) (true)
3. \(6 + 10 = 16 > 2\) (true)
Since \(2 + 6\) is not greater than 10, these lengths do not form a triangle.
Therefore, while the calculation for the perimeter is 18 inches, the given lengths do not constitute a valid triangle.