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M10-31

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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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Official Solution:


See the diagram below:

Image

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.


Answer: C
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Re: M10-31 [#permalink]

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New post 21 Jul 2016, 21:57
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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New post 26 Jul 2016, 04:41
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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New post 24 Nov 2016, 07:03
Please could you draw the graph to be able to tack the solution ?
many thanks

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New post 24 Nov 2016, 07:18
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M10-31 [#permalink]

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New post 18 Sep 2017, 05:34
Good explanation. Thank you.

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Re: M10-31   [#permalink] 18 Sep 2017, 05:34
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