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# What is the perimeter of right triangle ABC? (1) AB = 5 (2)

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Manager
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What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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01 Jun 2011, 07:07
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What is the perimeter of right triangle ABC?

(1) AB = 5
(2) AC = $$5\sqrt{2}$$
[Reveal] Spoiler: OA

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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01 Jun 2011, 07:27
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dreambeliever wrote:
What is the perimeter of right triangle ABC?
(1) AB = 5
(2) AC = $$5\sqrt{2}$$

(1) AB=5
We can't know the perimeter just by knowing one side of the right triangle.
Not Sufficient.

(2) $$AC=5\sqrt{2}$$
Not Sufficient.

Combining both;
We don't know which side is the hypotenuse.

If
$$AC=Hypotenuse=5\sqrt{2}$$
$$AB=5$$
$$BC=5$$
$$Perimeter=10+5\sqrt{2}$$

If
$$BC=hypotenuse$$
$$AB=5$$
$$AC=5\sqrt{2}$$
$$BC^2=AB^2+AC^2$$
$$BC^2=25+50$$
$$BC=\sqrt{75}=5\sqrt{3}$$
$$Perimeter=5+5\sqrt{2}+5\sqrt{3}$$

Not Sufficient.

Ans: "E"
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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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01 Jun 2011, 07:32
OA is E.

But for some reason I remember learning in my High School that a right angled triangle ABC is right angled at B. If it was right angled at C, then the triangle will be referred to as ACB. Does that convention not apply to the GMAT?

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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01 Jun 2011, 07:53
dreambeliever wrote:
OA is E.

But for some reason I remember learning in my High School that a right angled triangle ABC is right angled at B. If it was right angled at C, then the triangle will be referred to as ACB. Does that convention not apply to the GMAT?

I would expect GMAT to explicitly tell me at which angle the triangle is right angled. I leave this for some experts to answer.
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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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06 Jun 2011, 03:02
Since which angle is right angle has not been mentioned.

5(2^1/2 -1) < BC < 5(2^1/2 + 1).

perimeter can be anything is this region.

Thus E.
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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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06 Jun 2011, 18:57
yes, it is a trap. Don't assume anything on GMAT!

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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07 Jun 2011, 11:53
dreambeliever wrote:
But for some reason I remember learning in my High School that a right angled triangle ABC is right angled at B. If it was right angled at C, then the triangle will be referred to as ACB. Does that convention not apply to the GMAT?

That's not a convention I've ever heard of. Don't assume that on the GMAT, at least.
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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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28 Sep 2015, 08:59
since we do not know which angle is right angle, there are two possibilities. hence option is E.

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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25 Oct 2015, 07:30
Doesn't the 30-60-90 rule apply here?

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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25 Oct 2015, 07:34
roopika2990 wrote:
Doesn't the 30-60-90 rule apply here?

Without knowing which angle is 90 degrees, how can you be sure of this? Additionally, why would you apply 30-60-90 rule here? Can you mention more about your thought process?
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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]

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20 Sep 2016, 08:25
E is correct. Here's why:

(1) AB = 5 --> NOT SUFFICIENT - you can't figure out perimeter of a triangle with only one side and no further information

(2) AC = 5√2 --> NOT SUFFICIENT - same as (1)

A,B,D are eliminated

Together (1) + (2) --> NOT SUFFICIENT - we don't know what is the hypotenuse and which is a side, therefore we don't know how to set up pythagorean theorem to find the missing side.

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Re: What is the perimeter of right triangle ABC? (1) AB = 5 (2)   [#permalink] 20 Sep 2016, 08:25
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