SOLUTION: Given side lengths 4 units, 8 units, and x units, determine the range in which x must lie in order for a triangle to exist.

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Question 731564: Given side lengths 4 units, 8 units, and x units, determine the range in which x must lie in order for a triangle to exist.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a triangle, the length of one side is less than the sum of the lengths of the other two sides.
So,
x%3C4%2B8 --> x%3C12 to begin with.
Also,
8%3Cx%2B4 --> 8-4%3Cx --> 4%3Cx
Considering those two inequalities together tells us that
highlight%284%3Cx%3C12%29 so x is between 4 and 12.

NOTE:
Why is it that in a triangle, the length of one side is less than the sum of the lengths of the other two sides?
That is because the "one side" is the "straight line" connecting two vertices, and its length is the distance between those two points measured along the straight line.
The sum of the lengths of the other two sides is the distance between the same two vertices when you go the long way, making a stop over at the third vertex.