triangle inequality

Question

-1

1328

2

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

Guest Mar 26, 2020

CoolStuffYT · Answer 1 · 2020-03-26T01:33:14

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!)

geno3141 · Answer 2 · 2020-03-26T02:47:57

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.