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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<18
b) 13<p<22
c) 13<p<26
d) 18<p<22
e) 18<p<26



User Bmhkim
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1 Answer

6 votes

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.


User Dave Jellison
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