if you have a triangle, and one side is 3 inch, other is 4. what is the largest and smallest possible lengths for the 3rd side?

Question

if you have a triangle, and one side is 3 inch, other is 4.  what is the largest and smallest possible lengths for the 3rd side?

anonymous · Answer

Well you know the 3rd side cannot be larger than 3 + 4 from the triangle inequality

s < 3 + 4
s < 7

So 7 is an upper bound.  The length can be as close to 7 as you desire but it cannot be 7.

As for the smallest length, consider what happens as the third side gets smaller and smaller.  It would appear that s approaches 4 - 3 = 1.  In fact, when you overlap the two sides, that leaves a distance of 1.  This 1 serves as our lower bound.  I.e., the third length can approach 1 but never reach it.

anonymous · Answer

I should also state that the 3rd side cannot be equal to 3 + 4 either***

anonymous · Answer

so the largest is 7 and smalled is 1? 
i also have to do 2in and 3in.  so that would be 5 and1?

anonymous · Answer

They are boundary points.  The third side can be 6.9999999999999999, so long as it is less than 7.  There is no 'maximum' length as you can always pick a side closer and closer to 7.

7 is a limit that the side can never reach.

anonymous · Answer

Unless you consider a triangle with two sides overlapping, but then it wouldn't be a triangle anymore.

anonymous · Answer

ok, dude, you are awesome :) so you get a medal and a fan :) congratz, lol

anonymous · Answer

For similar reasons, the boundaries for the other triangle would be a lower limit of 1 and an upper limit of 5.  But these limits can never be reached.