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In the triangle shown, n is a positive integer, and \(\angle A > \angle B > \angle C\). How many possible values of n are there?

 Mar 26, 2020
 #1
avatar+1116 
+2

Answer: \(\frac{8}{3}

 

Explanation:

The largest angle's opposite side is the largest length of the triangle.

So \(2n+12>2n+7>3n-3\).

Take the last two inequalities and get \(n<10\)

Additionally, we can apply the triangle inequality and get \(2n+7+3n-3>2n+12\)

Solve to get \(3n>8\), and n>8/3.

So \(\frac{8}{3} .

 

You are very welcome!

:P

 

(I'm not completely sure about my answer, if someone could double check that would be great!)

 Mar 26, 2020
 #2
avatar+21017 
+1

I agree with CoolStuffYT that  n  >  8/3  and that  n  <  10.

 

Now, to finish you will need to count the positive integers between these two limits.

 Mar 26, 2020

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