Question
Find the perimeter of a triangle where one side is 2 in. One side is 6in. And the other side is 10 in.
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 are 2 inches, 6 inches, and 10 inches.
\[
\text{Perimeter} = 2 \, \text{in} + 6 \, \text{in} + 10 \, \text{in} = 18 \, \text{in}
\]
However, it's important to note that these side lengths do not actually form a triangle, as they violate the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Here:
- \(2 + 6 = 8\) which is not greater than \(10\).
Thus, a triangle cannot be formed with these side lengths. The perimeter is effectively not applicable since a triangle cannot exist with these dimensions.
\[
\text{Perimeter} = 2 \, \text{in} + 6 \, \text{in} + 10 \, \text{in} = 18 \, \text{in}
\]
However, it's important to note that these side lengths do not actually form a triangle, as they violate the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Here:
- \(2 + 6 = 8\) which is not greater than \(10\).
Thus, a triangle cannot be formed with these side lengths. The perimeter is effectively not applicable since a triangle cannot exist with these dimensions.