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Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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23 00:00

Difficulty:   15% (low)

Question Stats: 78% (01:33) correct 22% (02:03) wrong based on 518 sessions

### HideShow timer Statistics Planning is in progress for a fenced, rectangular playground with an area of 1,600 square meters. The graph above shows the perimeter, in meters, as a function of the length of the playground. The length of the playground should be how many meters to minimize the perimeter and, therefore, the amount of fencing needed to enclose the playground?

A. 10
B. 40
C. 60
D. 160
E. 340

NEW question from GMAT® Quantitative Review 2019

(PS14060)

Attachment: shot28.jpg [ 14.9 KiB | Viewed 5273 times ]

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##### Most Helpful Community Reply
Senior Manager  D
Joined: 18 Jun 2018
Posts: 267
Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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3
3
Bunuel wrote: Planning is in progress for a fenced, rectangular playground with an area of 1,600 square meters. The graph above shows the perimeter, in meters, as a function of the length of the playground. The length of the playground should be how many meters to minimize the perimeter and, therefore, the amount of fencing needed to enclose the playground?

A. 10
B. 40
C. 60
D. 160
E. 340

NEW question from GMAT® Quantitative Review 2019

(PS14060)

Attachment:
shot28.jpg

OA:B
Lowest point on the graph(40,160) where 40 is the length and 160 is perimeter.
So length should be 40
This matches with
Quote:
Among all rectangles of given area, the square has the least perimeter.

Given Area = $$1600 m^2$$
For perimeter to be least, it should be square with side a.
$$a^2=1600m^2$$
$$a=40 m$$
$$Perimeter =4a =4*40 =160 m$$
##### General Discussion
Intern  Joined: 11 Jul 2018
Posts: 19
Re: Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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1
Lowest point on the graph is 40, 160
i.e. Length = 40 and Perimeter = 160

This is lowest for both Length as well as perimeter.

Answer B.

But this looks like a trick question and may have some hidden meaning Intern  B
Joined: 03 Sep 2017
Posts: 13
Location: Canada
GMAT 1: 650 Q46 V34 Re: Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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1
Answer is B. The graph seems a distraction as you can backsolve to get an answer. Also Square has the least perimeter when it comes to Polygons so B jumps out at you
Intern  Joined: 20 Jul 2017
Posts: 2
Schools: DeGroote'21 (A)
Re: Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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bangu wrote:
Lowest point on the graph is 40, 160
i.e. Length = 40 and Perimeter = 160

This is lowest for both Length as well as perimeter.

Answer B.

But this looks like a trick question and may have some hidden meaning To minimize perimeter i.e the rectangle must become a square
Therefore a^2=1600 . =>a=40
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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Hi All,

While this prompt is wordy, the relevant facts are not too hard to pull out. We're told that a rectangular playground will have an area of 1,600 square meters and we want to MINIMIZE the perimeter of the playground. We're asked for the LENGTH of the playground under those circumstances.

This question is based on a relatively rare Geometry rule. When given a 'fixed' area, the smallest perimeter of a rectangle that will have that exact area will occur when the shape is actually a SQUARE. You can actually prove this with a bit of experimentation:

A 1 meter x 1600 meter rectangle would have a perimeter of 3202 meters
A 2 meter x 800 meter rectangle would have a perimeter of 1604 meters
A 4 meter x 400 meter rectangle would have a perimeter of 808 meters
....
Etc.
A 40 meter x 40 meter rectangle would have a perimeter of 1600 meters

With an area of 1600 square meters, the square would have dimensions of 40 meters x 40 meters --> meaning that the 'length' would be 40.

Final Answer:

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Rich
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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Originally posted by EMPOWERgmatRichC on 15 Nov 2018, 23:20. Last edited by EMPOWERgmatRichC on 16 Nov 2018, 14:54, edited 1 time in total. SVP  V Joined: 26 Mar 2013 Posts: 2184 Re: Planning is in progress for a fenced, rectangular playground with an a [#permalink] ### Show Tags EMPOWERgmatRichC wrote: Hi All, While this prompt is wordy, the relevant facts are not too hard to pull out. We're told that a rectangular playground will have an area of 1,600 square meters and we want to MINIMIZE the perimeter of the playground. We're asked for the LENGTH of the playground under those circumstances. This question is based on a relatively rare Geometry rule. When given a 'fixed' area, the smallest perimeter of a rectangle that will have that exact area will occur when the shape is actually a SQUARE. You can actually prove this with a bit of experimentation: A 1 meter x 1600 meter rectangle would have a perimeter of 3202 meters A 2 meter x 800 meter rectangle would have a perimeter of 1604 meters A 4 meter x 400 meter rectangle would have a perimeter of 808 meters .... Etc. A 40 meter x400 meter rectangle would have a perimeter of 160 meters With an area of 1600 square meters, the square would have dimensions of 40 meters x 40 meters --> meaning that the 'length' would be 40. Final Answer: GMAT assassins aren't born, they're made, Rich Hi EMPOWERgmatRichC I thin there is a small typo highlighted. It must be 40. Also, I have a question. Why did not you use the graph attached with the question? is something tricky or wrong? Thanks in advance CEO  V Joined: 12 Sep 2015 Posts: 3727 Location: Canada Re: Planning is in progress for a fenced, rectangular playground with an a [#permalink] ### Show Tags 1 Top Contributor Bunuel wrote: Planning is in progress for a fenced, rectangular playground with an area of 1,600 square meters. The graph above shows the perimeter, in meters, as a function of the length of the playground. The length of the playground should be how many meters to minimize the perimeter and, therefore, the amount of fencing needed to enclose the playground? A. 10 B. 40 C. 60 D. 160 E. 340 Attachment: shot28.jpg It's a good idea to first try to understand what the graph is telling us. For example, the leftmost point on the curve has the coordinates (10, 340) This tells us that, if the length of the playground is 10 meters, then a total of 340 meters of fencing is required. This makes sense, since we want the playground to have an area of 1600 square meters. So, if the length of the rectangular playground is 10 meters, the width must be 160 meters (since this will give us an area of 1600) If the length and width are 10 and 160, then the perimeter = 10 + 10 + 160 + 160 = 340 Our goal is to MINIMIZE the perimeter. So, when we examine the points on the curve, we must find the point with the smallest y-coordinate, since the y-coordinate represents the perimeter of the fence. We can see the perimeter is minimized at the point (40, 160). This point tells us that, when the playground has length 40 meters, the perimeter is a mere 160 meters. Answer: B Cheers, Brent _________________ EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14198 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Planning is in progress for a fenced, rectangular playground with an a [#permalink] ### Show Tags Mo2men wrote: EMPOWERgmatRichC wrote: Hi All, While this prompt is wordy, the relevant facts are not too hard to pull out. We're told that a rectangular playground will have an area of 1,600 square meters and we want to MINIMIZE the perimeter of the playground. We're asked for the LENGTH of the playground under those circumstances. This question is based on a relatively rare Geometry rule. When given a 'fixed' area, the smallest perimeter of a rectangle that will have that exact area will occur when the shape is actually a SQUARE. You can actually prove this with a bit of experimentation: A 1 meter x 1600 meter rectangle would have a perimeter of 3202 meters A 2 meter x 800 meter rectangle would have a perimeter of 1604 meters A 4 meter x 400 meter rectangle would have a perimeter of 808 meters .... Etc. A 40 meter x400 meter rectangle would have a perimeter of 160 meters With an area of 1600 square meters, the square would have dimensions of 40 meters x 40 meters --> meaning that the 'length' would be 40. Final Answer: GMAT assassins aren't born, they're made, Rich Hi EMPOWERgmatRichC I thin there is a small typo highlighted. It must be 40. Also, I have a question. Why did not you use the graph attached with the question? is something tricky or wrong? Thanks in advance Hi Mo2men, The graph is perfectly fine - and using the data within can get you to the correct answer without too much trouble. In my explanation, I opted to focus on the underlying math rule behind why this math 'works' - since while it is a relatively rare rule, you are more likely to see that rule than you are to see anything like this graph on Test Day. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Re: Planning is in progress for a fenced, rectangular playground with an a  [#permalink]

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Bunuel wrote: Planning is in progress for a fenced, rectangular playground with an area of 1,600 square meters. The graph above shows the perimeter, in meters, as a function of the length of the playground. The length of the playground should be how many meters to minimize the perimeter and, therefore, the amount of fencing needed to enclose the playground?

A. 10
B. 40
C. 60
D. 160
E. 340

NEW question from GMAT® Quantitative Review 2019

(PS14060)

Attachment:
shot28.jpg

From the graph, we see that the lowest point on the graph is (40, 160), which means if the playground is 40 meters long, then its perimeter will be at its minimum, which is 160 meters.

Answer: B
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# Planning is in progress for a fenced, rectangular playground with an a

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