You have two pieces of wood that will make up two sides of a triangular picture frame. One is 6 in. long and the other is 7 in. long. What is the range of the possible lengths for the third side of the frame?

I don't remember learning about finding the range of possible lengths...

Question

You have two pieces of wood that will make up two sides of a triangular picture frame. One is 6 in. long and the other is 7 in. long. What is the range of the possible lengths for the third side of the frame? 

I don't remember learning about finding the range of possible lengths...

perl · Answer

you can use the triangle inequality

perl · Answer

the triangle inequality, suppose the three sides are a,b,c. the inequality theorem says the sum of any two sides must be greater than the third side

perl · Answer

, this is an inequality

anonymous · Answer

Yes, but how would I answer the question? I have several like this one but I don't get the range part. How would I use that?

anonymous · Answer

Wait, all I would have to do is make sure its less then the sum right?

perl · Answer

so if a,b,c are the three sides of a triangle we have 
a+ b > c 
a + c > b 
b + c > a

perl · Answer

you are given 6,7,x for the sides of your triangle, since we don't know the third side

perl · Answer

6 + 7 > x
6 + x > 7
x + 7 > 6

perl · Answer

solving this we get x > 1 , x < 13 
x is between 1 and 13

anonymous · Answer

That problem was a lot harder then I thought it was. I could of done that mentally. Thank you so much!

perl · Answer

thanks, and to show your appreciate ,  you can click best response

anonymous · Answer

Haha, thanks