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Mathematics

1 answer:

Arada [10]2 years ago

5 0

Check the picture below.

we have three sides, let's look at the two smaller sides first, 14 and 25.

check the picture atop

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side? Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 25 - 14 = 11. However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle. So whatever the third side may be, it must be greater than 11.

check the picture below

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 14 + 25 = 39 However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle. So whatever the third side may be, it must be less than 39. So 40 is clearly a no dice.

now we can do the same to hmmm ohh any of the other sets, say 10, 19 and 26, well, 19 - 10 = 9, and 10 + 19 = 29, so the 3rd side must be greater than 9 and less than 29, however 26 is fine, because is within that range, same for the other two sets if you wish to check them.