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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]

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10 Oct 2005, 07:34
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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 ΙΙI
[Reveal] Spoiler: OA

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Regards, S

Last edited by Bunuel on 31 Jul 2012, 11:26, edited 1 time in total.
Edited the question and added the OA.

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Re: PS Sides of a triangle [#permalink]

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10 Oct 2005, 07:42
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saurya_s wrote:
15. 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) ?I only
(B) ?II only
(C) I and ?I only
(D) II and ?II only
(E) I, ??, and ???

Plz explain.
Thanks

the rest side x must satisfy : 8-3<x< 8+3 <==> 5<x<11
B.

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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31 Jul 2012, 11:34
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shreya717 wrote:
Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?

I don't quite understand what you mean by the red part above. Anyway:

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 ΙΙI

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, $$(8-3)<x<(8+3)$$ --> $$5<x<11$$. Hence 5 and 11 cannot be the length of the third side, while 8 can be.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
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10 Oct 2005, 07:44
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the sum of the two sides must be greater than the third side. 3+8 =11
the difference of the two sides mut be less than the third side. 8-3=5

therefore the third side is between 5 and 11. Only B fulfills this.

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10 Oct 2005, 07:43
Quote:
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) ?I only
(B) ?II only
(C) I and ?I only
(D) II and ?II only
(E) I, ??, and ???

I and II only. Therefore the correct answer is C

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10 Oct 2005, 09:21
Since the new side has to be less than the sum of the other two sides

Choosing 5 -
3, 8 is not possible as 3+5 leads to 8 - so the other side will have to be less than 8 (but we know it is 8). So 5 is not a correct side.

Choosing 8 -
3, 8, 8 is still valid - (isosceles triangle if I still remember how to spell those) as the sum of any two is still bigger than the other side.

So Choice B.

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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31 Jul 2012, 11:19
Can't we assume 5<x<11? what if it's an iscoceles triangle, in which case the third side could be equal to either of the two sides?

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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Re: If 3 and 8 are the lengths of two sides of a triangular [#permalink]

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22 Sep 2017, 22:31
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Re: If 3 and 8 are the lengths of two sides of a triangular   [#permalink] 22 Sep 2017, 22:31
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