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Help with Quant question

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onedergyal
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Help with Quant question [#permalink] New post   23 Dec 2012, 09:02
Hi,
Im working on an easy quant question but this book does not explain much, so I need your help!

The question is:

Parallelogram ABCD has an area of 52 sq centimeters, a height of 4 centimeters and an angle with measure 60 degrees. What is the perimeter of parallelogram ABCD?

my answer was 32 but the book has 26+(16 root 3/3)

since the area is 52, i got that the sides were 13, and 4 (given)... so the total perimeter is (13*2) + (4*2)

How did they get 16 root 3 / 3? ?
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mikemcgarry
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Re: Help with Quant question [#permalink] New post   23 Dec 2012, 20:49
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onedergyal wrote:
Hi,
Im working on an easy quant question but this book does not explain much, so I need your help! The question is:
Parallelogram ABCD has an area of 52 sq centimeters, a height of 4 centimeters and an angle with measure 60 degrees. What is the perimeter of parallelogram ABCD?

my answer was 32 but the book has 26+(16 root 3/3)

since the area is 52, i got that the sides were 13, and 4 (given)... so the total perimeter is (13*2) + (4*2)

How did they get 16 root 3 / 3? ?

I'm happy to help with this. :-)
Attachment:
parallelogram, area = 52.JPG
parallelogram, area = 52.JPG [ 24.19 KiB | Viewed 1580 times ]

First of all, it sounds like you were treating the situation as if it were a rectangle, not a parallelogram. If 4 is the height, then 4 would NOT be the "slant length" of the sides. In the diagram, BE = 4 but AB and CD do not equal 4. This is a very common mistake folks make about parallelograms. The "height" is not the length of the slant.

You correctly figured out, from the area, that AD = BC = 13.

To find the length of AB = CD, we have to use the properties of the 30-60-90 triangle. Here's a blog to refresh your memory on these:
https://magoosh.com/gmat/2012/the-gmats- ... triangles/

Triangle ABE is a 30-60-90 triangle. For the 30-60-90 triangle, we can remember
hypotenuse:2
short leg:1
long leg: sqrt(3)

We know the long leg, BE = 4 and we want the hypotenuse.

long leg/hypotenuse = sqrt(3)/2
4/(AB) = sqrt(3)/2
8 = (AB)*sqrt(3)
AB = 8/sqrt(3)
Now, because we have a radical in the denominator, we are going to use a procedure you may recall from algebra two: rationalizing the denominator. We will multiply both the numerator and the denominator by sqrt(3). This has the effect of removing the radical from the denominator.
AB = [8/sqrt(3)]*[sqrt(3)/sqrt(3)] = [8*sqrt(3)]/3

perimeter = 2*(AD) + 2*(AB) = 26 + [16*sqrt(3)]/3
Voila! The OA.

Does all this make sense?
Mike :-)
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onedergyal
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Re: Help with Quant question [#permalink] New post   27 Dec 2012, 12:10
thanks for the reply! i just noticed that there was a response... Here is where I'm lost
I get that in a 30/60/90 triangle that the angle across from 60 is (x root 3)... so since that value is 4, I set 4 = to x root 3, then solve for x... so the length of that side is (4/root3.. and since root3 is in the demonimator.. its 4root3?) , so X =4, and 2x =8?
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mikemcgarry
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Re: Help with Quant question [#permalink] New post   27 Dec 2012, 22:00
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onedergyal wrote:
thanks for the reply! i just noticed that there was a response... Here is where I'm lost
I get that in a 30/60/90 triangle that the angle across from 60 is (x root 3)... so since that value is 4, I set 4 = to x root 3, then solve for x... so the length of that side is (4/root3.. and since root3 is in the demonimator.. its 4root3? NO!) , so X =4, and 2x =8? NO!

When you divide by a root, you need to rationalize the denominator. This means you have to multiply both the numerator and the denominator by that root, so that the product in the denominator produces an integer. Rationalizing the denominator is a very important procedure to understand for GMAT math. It is absolutely 100% false that 4/sqrt(3) is the same as, or anything even vaguely related to, 4*sqrt(3). Furthermore, the sqrt(3)'s do not simply cancel and disappear. Rather
Attachment:
four over root three.JPG
four over root three.JPG [ 11.92 KiB | Viewed 1526 times ]

That cannot be simplified any further. That expression on the right is the absolutely simplest mathematical form in which we can write this value. Since this is what x is, 2x would be twice this ------ 8*sqrt(3)/3
Does this make sense?
Mike :-)
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Re: Help with Quant question [#permalink]
27 Dec 2012, 22:00

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