Since all three inequalities hold true, we can conclude that it is possible to draw a triangle with side lengths of 3 meters, 4 meters, and 6 meters.
How to determine whether it is possible to draw a triangle with given side lengths
To determine whether it is possible to draw a triangle with side lengths of 3 meters, 4 meters, and 6 meters, apply the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, consider the three side lengths:
a = 3 meters
b = 4 meters
c = 6 meters
Now, check if the triangle inequality holds for these side lengths:
a + b > c
3 + 4 > 6
7 > 6
b + c > a
4 + 6 > 3
10 > 3
c + a > b
6 + 3 > 4
9 > 4
Since all three inequalities hold true, we can conclude that it is possible to draw a triangle with side lengths of 3 meters, 4 meters, and 6 meters.