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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]

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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, 02:36, edited 1 time in total.
Edited the question and added the OA.
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C

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]

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New post 18 Jul 2012, 23:15
(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]

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New post 19 Jul 2012, 02:50
Expert's post
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]

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New post 06 Sep 2013, 04:25
Now it is clear to me. Thanks
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Re: What is the perimeter of isosceles triangle ABC? [#permalink]

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Why is a side less than the sum of two sides? Check this figure out !
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TriangleInequality.svg.png
TriangleInequality.svg.png [ 46.39 KiB | Viewed 5867 times ]

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Re: What is the perimeter of isosceles triangle ABC? [#permalink]

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New post 11 Jul 2015, 02:11
Bunuel wrote:
(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.


Could I also say that given that AB = 9 and BC = 4 the third side can not be equal to 4 as 9 (AB) - 4 (BC) = 5 and then the third side would be smaller than the sum of the two others?
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Re: What is the perimeter of isosceles triangle ABC? [#permalink]

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New post 11 Jul 2015, 02:31
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noTh1ng wrote:
Bunuel wrote:
(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.


Could I also say that given that AB = 9 and BC = 4 the third side can not be equal to 4 as 9 (AB) - 4 (BC) = 5 and then the third side would be smaller than the sum of the two others?


Yes, that's correct:
(9 - 4) < (third side) < (9 + 4)
5 < (third side) < 13.
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Re: What is the perimeter of isosceles triangle ABC? [#permalink]

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New post 19 Dec 2015, 22:06
Sum of two sides should be greater than the third side
Difference of two sides should be less than the third sides.

Statement 1 gives a side length but puts into question whether this is one of the two same sized sides of an isosceles triangles.
Statement 2 follows the same path.

Using the two statements and applying the two properties about sum and difference of two sides, we can deduce that 4 cannot be one of the two equal sides. THe two equal sides measure 9. Hence C.
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Re: What is the perimeter of isosceles triangle ABC? [#permalink]

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New post 28 Dec 2015, 03:35
Brunel, is there a formula to find Area of an isosceles triangle if we are given only the Perimeter of that Triangle ?

Thanks in Advance
Re: What is the perimeter of isosceles triangle ABC?   [#permalink] 28 Dec 2015, 03:35
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