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If 3 and 8 are the lengths of two sides of a triangular

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If 3 and 8 are the lengths of two sides of a triangular [#permalink] New post 15 Dec 2007, 11:29
If 3 and 8 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?



I. 5

II. 8

III. 11



(A) ΙI only

(B) ΙII only

(C) I and ΙI only

(D) II and ΙII only

(E) I, ΙΙ, and ΙΙ
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 [#permalink] New post 15 Dec 2007, 12:34
Expert's post
(incorrect)

C

a=3, b=8 ==> c e (0,a+b) ==> c e (0,11)
So 5,8 can be but 11 cannot

Last edited by walker on 15 Dec 2007, 14:02, edited 1 time in total.
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 [#permalink] New post 15 Dec 2007, 13:14
Agree with A. Only 8 works here.

It can't be 11 because 3+8 = 11. The other two sides would need to be connected in a straight line to reach that length. You can't have a triangle without angles!

It can't be 5 because 8-3 = 5. If there were any angle at all between the 8 and 3 sides then 5 wouldn't reach back to the other side.

You have a 8" long piece of string. You tie a 3" long piece of string on to one end. The only way you can have a 5" piece of string connect the two ends is if the 3" piece is laying across the 8" going back in that direction. Once again that's not a triangle, but a straight line made up of 3 pieces of string.

The equation here is

the smallest side must be greater than 8-3 = 5 so x > 5
the largest side must be smaller than 8+3 = 11 so x < 11

8 falls between 5 and 11, but the other two aren't in between these parameters.
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 [#permalink] New post 15 Dec 2007, 14:02
Expert's post
Agree with A.

c should be e (5,11)
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 [#permalink] New post 16 Dec 2007, 00:20
OA is A. Only 5 is right but I do not know why...
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 [#permalink] New post 16 Dec 2007, 00:32
Hi,
The rule is that the sum of ANY two sides of a triangle is always bigger than the third side.
Hope it helps
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 [#permalink] New post 16 Dec 2007, 06:23
marcodonzelli wrote:
OA is A. Only 5 is right but I do not know why...


Choice A is only 8 is correct :-D
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 [#permalink] New post 16 Dec 2007, 07:53
the rule is that the sum two smaller sides of the triangle must be greater than the largest side.

hence if the sides are 3 and 8 then the only answer that will work is 8.

3 + 8 is greater than 8
3 + 5 is NOT greater than 8
3 + 8 is NOT greater than 8

hope that makes sense
  [#permalink] 16 Dec 2007, 07:53
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