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 Post subject: Deceptive Geometry ProblemPosted: Tue Aug 03, 2010 6:04 pm

Joined: Tue Aug 03, 2010 4:21 pm
Posts: 2
Here is a geometry problem that typifies what GMAT test writers like to do, take a simple concept and point you toward the wrong answer.

An isosceles right triangle has a perimeter of 16 + 16 sq rt 2.

The question then asks for the measure of side x and in the drawing side x is NOT the hypotenuse.

A) 8

B) 8 sq rt 2

C) 16

D) 16 sq rt 2

E) 32

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 Post subject: Re: Answer to Deceptive Geometry ProblemPosted: Wed Aug 04, 2010 12:09 pm

Joined: Tue Aug 03, 2010 4:21 pm
Posts: 2
Remember that according to the "third side rule" any two sides of a triangle added together must be longer than the third side is alone.

That means that since the perimeter of this triangle is 16 + 16 sq rt 2 and since 16 sq rt 2 is the larger number - that must be the length of the two 45 degree sides not the hypotenuse. So 2x = 16 sq rt 2. So one side is 8 sq rt 2 and this is the correct answer. You can then check your result by multiplying that number - the side opposite a 45 degree angle by the sq rt of 2 and this should give you the length of the hypotenuse. In this case it does 8 sq rt 2 times sq rt 2 gives you 16.

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