The sum of the 2 smallest sides of a triangle must be greater than the length of its longest side
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5 < x < 9
4 < x < 20
Ok, well let me start you off with an example first. Suppose you have triangle ABC with side lengths 6 and 15. What is the range of the possible values of the third side? What I would do first is sketch a picture of triangle ABC and assign 6 and 15 to any two sides, it doesn't matter what two sides and I'll show you why in a moment. To solve this problem, you need to set up an inequality using the Triangle Inequality Theorem. This theorem simply states that any two sides of a triangle must add up to be greater than the third side. To do this, we need to set up two inequalities: 6 + 15 < x and 6 + x > 15. Simplify both those inequalities to solve for x. You should get x>21 and x>9. Now, all you need to do is set up a compound inequality using those two inequalities you just simplified and you should get: 9<x<21 Easy right? :)
Ah hah! That little word "which" is pretty much a giveaway ... I'll just bet there wassome kind of a list of choices that was supposed to go along with the question, butsomehow got lost.Anyway, the correct inequality is: 3 < x < 13 .
The range is just the difference between the largest and smallest values lowest (0) and highest (6) for a range of 6.