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

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Senior Manager
Joined: 08 Jul 2004
Posts: 437
If 3 and 8 are the lengths of two sides of a triangular  [#permalink]

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Updated on: 31 Jul 2012, 11:26
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65% (00:40) correct 35% (00:53) wrong based on 665 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) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI

Originally posted by saurya_s on 10 Oct 2005, 07:34.
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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Posts: 60605
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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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.
##### General Discussion
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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, 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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10 Dec 2019, 13:40
Hi All,

We're told that 3 and 8 are the lengths of two sides of a triangular region. We're asked which of the following values (3, 8 and 11) could be the length of the third side. This question is based on the Triangle Inequality Theorem and requires just a little Arithmetic to solve.

To start, when you have two sides of a triangle, the SMALLEST the third side could be would be just a little bit MORE than the DIFFERENCE of the two sides you have. Here, that's 8 - 3 = 5. If the third side was EXACTLY 5, then you would NOT have a triangle - you'd have a line of 8 on top of another line of 8. By making that third side just a little bigger than 5, you would then have a triangle.

In that same way, the LARGEST the third side could be would be just a little bit LESS than the SUM of the two sides. Here, that's 3 + 8 = 11. If the third side was EXACTLY 11, then you would NOT have a triangle - you'd have a line of 11 on top of another line of 11. By making that third side just a little less than 11, you would then have a triangle.

Thus, that third side falls into the following range: 3 < third side < 11. Based on the three given options, only a side of 8 is possible.

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Re: If 3 and 8 are the lengths of two sides of a triangular   [#permalink] 10 Dec 2019, 13:40
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