## TheForbiddenFollower 2 years ago 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?

1. LogicalApple

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.

2. LogicalApple

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

3. TheForbiddenFollower

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

4. LogicalApple

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.

5. LogicalApple

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

6. TheForbiddenFollower

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

7. LogicalApple

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.