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# If 3 and 8 are the lengths of two sides of a triangular region, which

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Math Expert
Joined: 02 Sep 2009
Posts: 55148
If 3 and 8 are the lengths of two sides of a triangular region, which  [#permalink]

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24 Aug 2017, 23:37
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71% (00:34) correct 29% (00:35) wrong based on 41 sessions

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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) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

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

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24 Aug 2017, 23:57
Bunuel wrote:
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) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

The only possibility for the third side of the triangle is 8
because the property of the triangle which is used over here is
the sum of any 2 sides must be larger than the third side.

Hence Option A(II only) is the answer choice
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Re: If 3 and 8 are the lengths of two sides of a triangular region, which  [#permalink]

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25 Aug 2017, 00:08
Bunuel wrote:
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) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

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.
Only possible value is 8 as 5<third side<11

A
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If 3 and 8 are the lengths of two sides of a triangular region, which  [#permalink]

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25 Aug 2017, 19:13
Bunuel wrote:
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) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

The third side of a triangle is always shorter than the sum of the other two sides:

x < 3 + 8
x < 11

AND the third side must be greater than the difference between the other two sides

x > 8 - 3
x > 5
5 < x

Together:

5 < x < 11

Third side x cannot be 5 or 11.

Only Option II satisfies the triangle inequality theorem.

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If 3 and 8 are the lengths of two sides of a triangular region, which   [#permalink] 25 Aug 2017, 19:13
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