Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Geometry Questions Please Help

Can you guys please help me with these problems?

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

Last edited by Oran2009 (2016-06-13 14:43:20)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Questions Please Help

Hi;

Hopefully someone else will see that diagram, I can not.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Re: Geometry Questions Please Help

I think I fixed the link. Try again

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Questions Please Help

I have placed the image in your post and I am getting 6 solutions for n.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Re: Geometry Questions Please Help

Thanks! But what is your solution, I wonder?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Questions Please Help

Start with the inequality;

3 n + 1 > 4 n - 9 which gives you an upper bound of n < 10. You already have a lower bound of n>0 given.

You can then refine the lower bound of n > 0 with the  inequality,

(3 n + 1) + (4 n - 9) > (3 n + 4) which tells you that n > 3.

Now I just checked n = 4,5,6,7,8,9. Found that they all worked and so there are 6 possible values of n.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry Questions Please Help

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