In order to be a triangle, the sum of two sides must be greater than the third side. (Just think about it for a bit and you will see why this has to be true). For example, could you have a triangle with side 3 inches, 4inches, and then a whopping 100 inches? No, because the other two sides are too short to fully connect a triangle!

So once you understand this, we can find the possible length of the missing side.

Let x be the length of the missing side in centimeters. The other two sides are 18cm and 40cm.

So one possible combination:

The sum of our two known lengths must be larger than the unknown length:

18 + 40 > x
58 > x

Therefore one constraint is that our third side has to be less than 58 centimeters.

Another combination:

18 + x > 40
x > 22

So another constraint is that our third side must be larger than 22 cm.

The last combination is pointless:

40 + x > 18

Since 40 is already larger than 18, then "40 + x" is obviously larger than 18.

So therefore our x has to be in this range:

22 < x < 58

In other words, our third side has to be larger than 22 cm, but less than 58 cm.

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3 years ago