Question 548738: I don't understand this problem please help.
Which set of integers cannot be lengths of the sides of a triangle?
1) {3,4,5}
2) {3,4,4}
3){2,3,4}
4) {3,1,1}
Answer by KMST(5396)   (Show Source):
You can put this solution on YOUR website! Imagine two segments, connected making an angle. Imagine that being two sides of a triangle. Imagine that you can manipulate that angle (not changing the length of the original segments) to make different triangles.
 As you make that angle larger and larger, the opposite side grows longer, but it is always shorter than the two other sides added up, because you are comparing the straight path between two vertices (the opposite side) to the path going around a corner (the angle). By the time the angle is 179°, those lengths are almost the same, but not quite. By the time the angle is 180°, your triangle has collapsed, with the long side on top of the other two. It is not a triangle any more. The longest opposite side that you can make is always less than the sum of the other two sides around your angle. So, you see that the longest side of a triangle can never measure quite as much as the sum of the lengths of the other two sides. It cannot measure more than the sum of the lengths of the other two sides. So you cannot make a triangle with the sides' lengths given in 4).
1), 2), and 3) will make some nice triangles (In fact 1) is a right triangle)
4) cannot make a triangle. Two sides with length 1 are too short for a third side with length 3.
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