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

Question

What is the perimeter of right triangle ABC?

(1) AB = 5
(2) AC =  5\sqrt{2}

fluke · Answer

(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"

dreambeliever · Answer

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?

fluke · Answer

I would expect GMAT to explicitly tell me at which angle the triangle is right angled. I leave this for some experts to answer.

amit2k9 · Answer

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.

brandy96 · Answer

yes, it is a trap. Don't assume anything on GMAT!

IanStewart · Answer

That's not a convention I've ever heard of. Don't assume that on the GMAT, at least.

brs1cob · Answer

since we do not know which angle is right angle, there are two possibilities. hence option is E.

roopika2990 · Answer

Doesn't the 30-60-90 rule apply here?

ENGRTOMBA2018 · Answer

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?

law258 · Answer

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.

bumpbot · Answer

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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)

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