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What is the perimeter of isosceles triangle ABC?

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What is the perimeter of isosceles triangle ABC? [#permalink] New post 31 Aug 2006, 23:41
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What is the perimeter of isosceles triangle ABC?

(1) The length of side AB is 9

(2) The length of side BC is 4
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Jul 2012, 01:36, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 01 Sep 2006, 00:34
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AB = 9 units
BC = 4 units
AC will have to be equal to 9 units. It cannot be 4 units because the length of the sum of two sides of a triangle must be greater than the third side and the problem states that the traingle is an isosceles triangle.
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Re: What is the perimeter of isosceles triangle ABC? (1) The [#permalink] New post 18 Jul 2012, 22:15
(1) AB = 9. We only know the length of one side. Not sufficient.
(2) BC = 4. We only know the length of one side. Not sufficient.

(1)+(2) If AB=AC=9 and BC=4 then the perimeter would be 9+9+4=22 but if AB=9 and AC=BC=4 then the perimeter would be 9+4+4=17. Not sufficient.

Answer: E.
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Re: What is the perimeter of isosceles triangle ABC? (1) The [#permalink] New post 19 Jul 2012, 01:50
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monirjewel wrote:
(1) AB = 9. We only know the length of one side. Not sufficient.
(2) BC = 4. We only know the length of one side. Not sufficient.

(1)+(2) If AB=AC=9 and BC=4 then the perimeter would be 9+9+4=22 but if AB=9 and AC=BC=4 then the perimeter would be 9+4+4=17. Not sufficient.

Answer: E.



Answer to this question should be C, not E.

What is the perimeter of isosceles triangle ABC?

(1) The length of side AB is 9. Clearly insufficient.

(2) The length of side BC is 4. Clearly insufficient.

(1)+(2) We know the lengths of the two sides of isosceles triangle ABC: AB=9 and BC=4, hence the length of AC is either 4 or 9. Relationship of the Sides of a Triangle: 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. Now, according to this, AC cannot equal to 4, because in this case the length of AB would be greater than the sum of the other two sides, AC and BC, (AB=9>AC+BC=4+4=8), hence AC=9 and P=9+9+4=22. Sufficient.

Answer: C.

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Re: What is the perimeter of isosceles triangle ABC? [#permalink] New post 06 Sep 2013, 03:25
Now it is clear to me. Thanks
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Re: What is the perimeter of isosceles triangle ABC? [#permalink] New post 13 Aug 2014, 05:39
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Why is a side less than the sum of two sides? Check this figure out !
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Re: What is the perimeter of isosceles triangle ABC?   [#permalink] 13 Aug 2014, 05:39
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