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M10-31

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:43
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Difficulty:

55% (hard)

Question Stats:

60% (00:56) correct 40% (01:04) wrong based on 98 sessions

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If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

(1) The base of the parallelogram is 10.

(2) One of the angles of the parallelogram is 45 degrees.
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139695 [0], given: 12794

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15 Sep 2014, 23:43
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Official Solution:

See the diagram below:

Given: $$Area=base*height=100$$. Question: $$P=2b+2l=?$$, where $$b$$ is the base and $$l$$ is the leg.

(1) The base of the parallelogram is 10. So, $$base=height=10$$. Infinitely many cases are possible. Look at the diagram (let the distance between two horizontal and vertical points be 10): all 4 parallelograms have $$base=height=10$$ but they have different perimeter. Not sufficient.

(2) One of the angles of the parallelogram is 45 degrees. Clearly insufficient. But from this statement height $$BX$$ and $$AX$$ will make isosceles right triangle: $$height=BX=AX$$.

(1)+(2) As from 2 we have that $$height=BX=AX$$ and from (1) we have that $$base=height=10$$, so $$AX=base=AD=10$$, which means that $$X$$ and $$D$$ coincide (case #4 on the diagram). Thus leg ($$AB$$) becomes hypotenuse of the isosceles right triangle with sides equal to 10, hence $$AB=10\sqrt{2}$$ and $$P=20+20\sqrt{2}$$. Sufficient.

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Schools: Kellogg '20 (S)
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21 Jul 2016, 20:57
If statement 1 gives us the base and height then we can simply values in 2l+2b and this should be sufficient?

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26 Jul 2016, 03:41
Why can't I use the second statement to calculate the length of the other side using sin 45. I know the height is 10. Shouldn't the answer be B?

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26 Jul 2016, 03:49
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rokr44 wrote:
Why can't I use the second statement to calculate the length of the other side using sin 45. I know the height is 10. Shouldn't the answer be B?

How do you know that height is 10 for (2)?
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24 Nov 2016, 06:03
Please could you draw the graph to be able to tack the solution ?
many thanks

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24 Nov 2016, 06:18
hatemnag wrote:
Please could you draw the graph to be able to tack the solution ?
many thanks

There is an image attached in the solution. If it's still not enough please check the following discussion: if-the-area-of-a-parallelogram-is-100-what-is-the-perimeter-80300.html

Hope it helps.
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18 Sep 2017, 04:34
Good explanation. Thank you.

Posted from my mobile device

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Re: M10-31   [#permalink] 18 Sep 2017, 04:34
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