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

Question

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

Bunuel · Accepted Answer

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) 5math-triangles-87197.html Hope it helps.

laxieqv · Answer

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

desiguy · Answer

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.

shreya717 · Answer

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?

pushpitkc · Answer

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

Luckisnoexcuse · Answer

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

generis · Answer

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

EMPOWERgmatRichC · Answer

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:  A

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

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,
Brent

bumpbot · Answer

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

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

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