If a triangle has sides of length 4, 9, and x, which of the following represents the range of values for the perimeter (p) of the triangle? a) 13< p< 18b) 13< p< 22c) 13< p< 26d) 18< p< 22e) 18< p< 26

Let us look at a few values for x

could x be 1?

That would mean that p = 4 + 9 + 1 = 14 which would satisfy to top 3 inequalities.

p would be > than 13. But would there be a triangle

The answer is no. 4 + 1 has to be greater than 9 and it isn't. That means that 13 is not the threshold for the perimeter. So 18 must be. that means that x is at least 5

How are you going to tell the difference between 22 and 26?

What will x be if the perimeter is 26?

4 + 9 + x = 26

13 + x = 26

x = 13 Will that work? This is the absolute limit of the perimeter.

if x = 12 then a triangle will be formed. So everything is fine.

the answer is e. <<<< answer.

The perimeter can be made just slightly less than 26 and you will have a triangle. If you have exactly 26 you will have 2 lines, one 13 units long and the other one 5 + 9 or 13 units long.

6.5

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you said it was in the question

~courtney

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