The three pieces of wood of considered measure would make no triangle because 2+3 = 5, and 5 < 6. This is correctly explained by student 1.
What is triangle inequality theorem?
Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]
If three line segments are such that their lengths satisfy the above three conditions, then they can form a triangle, else not.
For this case, the sides given are:
- a = 2 ft,
- b = 3 ft,
- and c = 6 ft
We see that:
a + b < 6 because 2+3 = 5, and 5 < 6
That means, sum of the sides which are of 2 ft and 3 ft is smaller than the third side of length 6 ft.
Thus, since these lengths are not satisfying triangle inequality, therefore, no triangle can be formed.
Thus, the three pieces of wood of considered measure would make no triangle because 2+3 = 5, and 5 < 6. This is correctly explained by student 1.
Learn more about triangle inequality theorem here:
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