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

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What is the perimeter of right triangle ABC? (1) AB = 5 (2) [#permalink]  01 Jun 2011, 06:07
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17% (01:31) correct 83% (00:32) wrong based on 15 sessions
What is the perimeter of right triangle ABC?
(1) AB = 5
(2) AC = $$5\sqrt{2}$$
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Re: right triangle perimeter [#permalink]  01 Jun 2011, 06:27
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: right triangle perimeter [#permalink]  01 Jun 2011, 06:32
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: right triangle perimeter [#permalink]  01 Jun 2011, 06:53
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: right triangle perimeter [#permalink]  06 Jun 2011, 02:02
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: right triangle perimeter [#permalink]  06 Jun 2011, 17:57
yes, it is a trap. Don't assume anything on GMAT!
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Re: right triangle perimeter [#permalink]  07 Jun 2011, 10:53
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: right triangle perimeter   [#permalink] 07 Jun 2011, 10:53
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