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Difficulty: 505-555 Level,    Geometry,                
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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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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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Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
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 region, which [#permalink]
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]
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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Re: If 3 and 8 are the lengths of two sides of a triangular region, which [#permalink]
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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.

Answer A
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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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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.

Final Answer:

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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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saurya_s 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) ΙI only
(B) ΙII only
(C) I and ΙI only
(D) II and ΙII only
(E) I, ΙΙ, and ΙΙI


IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

So, for this question: 8 - 3 < third side < 8 + 3
Simplify: 5 < third side < 11

So, the third side must be LONGER than 5 and SHORTER than 11
Answer: A

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