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 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?
 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?

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LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Well 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.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2I should also state that the 3rd side cannot be equal to 3 + 4 either***

TheForbiddenFollower
 2 years ago
Best ResponseYou've already chosen the best response.0so the largest is 7 and smalled is 1? i also have to do 2in and 3in. so that would be 5 and1?

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2They 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.

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2Unless you consider a triangle with two sides overlapping, but then it wouldn't be a triangle anymore.

TheForbiddenFollower
 2 years ago
Best ResponseYou've already chosen the best response.0ok, dude, you are awesome :) so you get a medal and a fan :) congratz, lol

LogicalApple
 2 years ago
Best ResponseYou've already chosen the best response.2For 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.
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