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Can someone explain how to find the length of triangles? I watched some videos and looked things up but none make sense. (with numbers so basically 12 cm, 13 cm, 24 cm. That kind of thing)

1 Answer

8 votes

Check the picture below, there are two cases, case of option B and case of option C for Lorelei, we are looking at only the two smaller sides.

on option B

we have sides of 12 and 13, now, if we move the sides closer and closer to be one on top of the other, what is left is just one unit of slack, because the side of 12 laying right on top of the side of 13, is short by 1 unit to be 13, however if we do that, we no longer have a triangle, just two pancaked lines, so whatever the 3rd side may be, it must be greater than 1 unit.

now, if we instead move the sides away from each other, to the extent that sides 12 and 13 make a flat line, well, a flat line will be as long as 12 + 13 = 25, however, we can't do that becuause, again if we do so, all we have is a flat-line, and no longer a triangle, so, whatever the 3rd side may be, it must be less than 25 units.

well, on option B, we have a 3rd side given as 25, but we can't use that, because we'd be losing our triangle, we'd only be left with a flat line, so no dice on B.

on option C

as you see in the picture, same thing, pancake one side on top of the other and there's no slack, so the 3rd side must be greater than 0.

now move the sides away from each other and their sum gives 10 + 10 = 20, so the 3rd side must be less than 20.

we're given a 3rd side of 24, how the dickens are we going to get a side to be 24 when both sides of 10 extended only give 20? not going to happen, so no dice on C.

needeless to say the sides of 12, and 14 provide for a 3rd side of greater than 2 and less than 26, well, 24 is indeed within that range.

Can someone explain how to find the length of triangles? I watched some videos and-example-1
User Dinesh Kannan
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