it possible to have a triangle whose lengths are 2 m, 6 m, and 11 m? Justify your answer.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, so the answer is .........
no
because 2+6 has to be greater than 11
great!
To determine if it is possible to have a triangle with lengths 2 m, 6 m, and 11 m, we can use 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. In other words, for a triangle with side lengths a, b, and c, the following equation must hold:
a + b > c
b + c > a
c + a > b
Let's substitute the given lengths into these equations:
2 + 6 > 11
6 + 11 > 2
11 + 2 > 6
Simplifying these equations:
8 > 11 (not true)
17 > 2 (true)
13 > 6 (true)
From the above equations, we can see that the sum of the lengths of 6 m and 11 m is greater than the length of 2 m. Similarly, the sum of the lengths of 2 m and 6 m is greater than the length of 11 m.
However, we cannot find a combination where the sum of the two smaller sides is greater than the longest side. Using the rule stated previously, we can conclude that it is not possible to have a triangle with side lengths 2 m, 6 m, and 11 m.
Therefore, the answer is no, it is not possible to have a triangle with lengths 2 m, 6 m, and 11 m.