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GMAT Software Geometry Question

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by mpaudena » Tue Mar 03, 2009 4:17 pm
Hello GMAT Beaters. First, thanks in advance for the response. Second, on the GMAT software I came upon a geometry question that goes as follows:

The perimeter of a certain isosceles triangle is 16 + 16(square root of 2). What is the length of the hypotenuse of the triangle?

I can't seem to figure out how they came up with the answer. Please help. Thanks.
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by crossingfingers » Tue Mar 03, 2009 5:29 pm
The perimeter of a right angled isosceles triangle is: 2a + b where 2a are the 2 equal sides and b is the unequal side...

we have 16 + 16 (sq root 2).

Now I used the POE:

if 2a=16 a=8...then b = 16(sq root 2) doesnt make sense

if 2a= 16(sq root 2) a=8(sq root 2)...then b=hyp=16 makes sense.
you can get it from the 1:1:sq root 2 property of an isosceles right triangle or u can use Pythagoras theorem to solve to check.

Not sure if this is the standard approach.
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by mpaudena » Tue Mar 03, 2009 5:37 pm
crossingfingers wrote:The perimeter of a right angled isosceles triangle is: 2a + b where 2a are the 2 equal sides and b is the unequal side...

we have 16 + 16 (sq root 2).

Now I used the POE:

if 2a=16 a=8...then b = 16(sq root 2) doesnt make sense

if 2a= 16(sq root 2) a=8(sq root 2)...then b=hyp=16 makes sense.
you can get it from the 1:1:sq root 2 property of an isosceles right triangle or u can use Pythagoras theorem to solve to check.

Not sure if this is the standard approach.
Thanks crossing fingers but first what is POE? Second, why did you think that the first choice didn't make sense? Is it cause you tried the properties of isoscelese and it didn't work?
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by mpaudena » Tue Mar 03, 2009 5:41 pm
Also does anyone know how to do this algebraically cause I'm sure this will not be the exact question on the test and I want to understand the concept that I'm missing. Thanks.
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by crossingfingers » Tue Mar 03, 2009 5:42 pm
oops...sorry...POE - process of elimination (am pretty much doing an either or)

yes...for the first choice applying Pythagoras theorem a^2 + a^2 = b^2...gives us sq root of (64 + 64) = 8(sq root of 2) which is not what's expected - 16(sq root of 2). Hence proceed to 2
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by mridula » Tue Mar 03, 2009 8:57 pm
what is the OA?
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by mpaudena » Wed Mar 04, 2009 2:26 am
Does anyone know how to do this algebraically cause I'm sure this will not be the exact question on the test and I want to understand the concept that I'm missing. Thanks.
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by farooq » Wed Mar 04, 2009 6:55 am
crossingfingers wrote:The perimeter of a right angled isosceles triangle is: 2a + b where 2a are the 2 equal sides and b is the unequal side...

we have 16 + 16 (sq root 2).

Now I used the POE:

if 2a=16 a=8...then b = 16(sq root 2) doesnt make sense

if 2a= 16(sq root 2) a=8(sq root 2)...then b=hyp=16 makes sense.
you can get it from the 1:1:sq root 2 property of an isosceles right triangle or u can use Pythagoras theorem to solve to check.

Not sure if this is the standard approach.
But where it is mentioned that the triangle is right angle triangle :(
Regards,
Farooq Farooqui.
London. UK

It is your Attitude, not your Aptitude, that determines your Altitude.
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by mpaudena » Wed Mar 04, 2009 7:41 am
farooq wrote:
crossingfingers wrote:The perimeter of a right angled isosceles triangle is: 2a + b where 2a are the 2 equal sides and b is the unequal side...

we have 16 + 16 (sq root 2).

Now I used the POE:

if 2a=16 a=8...then b = 16(sq root 2) doesnt make sense

if 2a= 16(sq root 2) a=8(sq root 2)...then b=hyp=16 makes sense.
you can get it from the 1:1:sq root 2 property of an isosceles right triangle or u can use Pythagoras theorem to solve to check.

Not sure if this is the standard approach.
But where it is mentioned that the triangle is right angle triangle :(
Sorry about that guys. I neglected to write that it was a right triangle. Crossingfingers was correct both in the answer and in that it was a right triangle.
Last edited by mpaudena on Wed Mar 04, 2009 3:08 pm, edited 1 time in total.
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by mkbigmoz » Wed Mar 04, 2009 2:59 pm
What was the answer? You can put it in a spoiler
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