A triangle has two sides of length 6 and 6. What value could the length of the third side be? Check all that apply. A. 36 B. 12 C. 10 D. 6 E. 3 F. 2

Question

hartnn · Answer

length of 3rd side of a triangle cannot be greater than sum of 2 sides, 
so, the length less than or = 6+6
does this help ?

anonymous · Answer

All the possible side lengths fit the following equation:
$$(Side A Length) + (Side B Length)\ge (Side C Length)$$

anonymous · Answer

It helps a lot thank you both

anonymous · Answer

I think

hartnn · Answer

welcome ^_^

anonymous · Answer

OOPS!  Should be less than or equal to.  Sorry!

hartnn · Answer

also, since i notice you are new here, i would like to welcome you.

$\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile$

anonymous · Answer

Welcome as well!

terenzreignz · Answer

@hartnn 
did you mean greater than or =?

anonymous · Answer

I meant less than or equal to

terenzreignz · Answer

Something about your first post feels kind of reversed...

anonymous · Answer

I screwed up

hartnn · Answer

:O 
how did i make such a mistake!!
i am sorry!
its gretaer than =

terenzreignz · Answer

I am content in the proof that @hartnn is human after all XD

anonymous · Answer

No worries

anonymous · Answer

Wait
I screwed up again
My first answer was right

terenzreignz · Answer

Or... I screwed up.

terenzreignz · Answer

I should have stayed mum XD

hartnn · Answer

don't over think,
The sum of the lengths of any two sides of a triangle always exceeds the length of the third side, a principle known as the triangle inequality

anonymous · Answer

No...  I didn't screw up.  $$6+6\neq12$$

anonymous · Answer

Would indicate I was wrong.  Since that equation is in and of itself wrong, I must be right.

anonymous · Answer

Im learning this stuff in my geometry class and i cant learn because of a first year teacher

anonymous · Answer

Hmm.  I had a first-year teacher and she was fantastic.

anonymous · Answer

This one is a young guy. He is still acting like a child

anonymous · Answer

Ah.  That could be a problem.

anonymous · Answer

Yeah and he's a handsome guy and he is distracted by getting alot of attention frow the girls in the class

terenzreignz · Answer

Getting a bit off topic ;)
Let's be general, then :D
If you're given two side lengths of a triangle, a and b, the possible values for the third side always fall within this interval:
$$\huge (|a-b| \ , \ a+b)$$

anonymous · Answer

LOL I had a teacher just like that this year, only he was gay so it was a bit interesting as I haven't the foggiest which one I am.  Also, @terenzreignz has a very good point.

anonymous · Answer

Yep lets get on topic

anonymous · Answer

Also, for your info, I am in fact a guy.

anonymous · Answer

And agreed.

terenzreignz · Answer

Don't I just love having good points :D
So, you see, @FradyCatt 
Using your first example, where a and b are both 6, then the possible values for the third side are in this interval...
(|6-6| , 6+6)=(0 , 12)
So, which values fall within that interval? You be the judge ;)

anonymous · Answer

I still think my first answer holds true.

hartnn · Answer

yes, it does.

terenzreignz · Answer

LOL that it does :D

anonymous · Answer

10, 6, 3, 2

terenzreignz · Answer

And those are your answers.  You may thank me later. ;)

anonymous · Answer

Or me!

hartnn · Answer

or me!

hartnn · Answer

lol

anonymous · Answer

Thank you all

anonymous · Answer

@hartnn , your first answer would have gotten him the problem wrong!

terenzreignz · Answer

Would it?

anonymous · Answer

'Twould.

hartnn · Answer

on sec, no. :P

anonymous · Answer

Better to not have to correct it.  Less confusion all around.

terenzreignz · Answer

It was correct o.O
Unless I'm missing something.

hartnn · Answer

yeah, it was..

hartnn · Answer

i got confused when you asked, 'greater than...'

anonymous · Answer

Yes, you are.  If you use less than, it's correct.  but if it's equal to, then the whole thing becomes a line.

anonymous · Answer

I was confused the whole time lol

anonymous · Answer

God, me too.

hartnn · Answer

sorry for confusion guys.

anonymous · Answer

No problem

anonymous · Answer

So, I'll attempt some finality.  Your answer must satisfy the following equation.
$$SideA+SideB > SideC$$

directrix · Answer

Triangle Inequality Theorem:
One side of a triangle has length less than the sum of the other two.

anonymous · Answer

Yes, we know.

terenzreignz · Answer

Finality? Because this interval is awesome, I'm going to write it one more time :D
Given the two side lengths a and b, the length of the third side must be in this interval
$$\large (|a-b| \ , \ a+b)$$

directrix · Answer

Yes, and the third side is greater than the positive difference of the other two sides as well.

In this case, (6-6) < 3rd side < (6 + 6)  @FradyCatt

anonymous · Answer

You don't need that long and complicated interval.  It just adds confusion.

terenzreignz · Answer

On the contrary, your criterion was rather insufficient, because the side C could be smaller than the positive difference of the two original sides.

anonymous · Answer

It could, but if you use common sense and discard 0 or negative answers, it works just fine.

terenzreignz · Answer

No, I meant, for instance, in a question he/she PM'ed me, given the two lengths 7 and 12
Using the criterion you gave, one of the choices, 3, fits it, but is certainly not a possible length of the third side.
It takes more than common sense to see that (methinks), so I think you have to consider the positive difference, and hence the interval.

anonymous · Answer

He i;m a he and my name is Josh

terenzreignz · Answer

I'm Terence.  Nice to meet you :)

anonymous · Answer

Nice to meet you too

anonymous · Answer

My name is Edward.  Nice to meet all of you.

anonymous · Answer

same to you