Planning is in progress for a fenced, rectangular playground with an a

Question

https://gmatclub.com/forum/download/file.php?id=42465 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) shot28.jpg

BrentGMATPrepNow · Accepted Answer

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

Bismarck · Answer

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
 
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

bangu · Answer

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

nrisbood · Answer

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

Sujay_k · Answer

To minimize perimeter i.e the rectangle must become a square 
Therefore a^2=1600 . =>a=40

EMPOWERgmatRichC · Answer

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 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:  B

GMAT assassins aren't born, they're made, 
Rich

Mo2men · Answer

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

EMPOWERgmatRichC · Answer

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

ScottTargetTestPrep · Answer

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

ueh55406 · Answer

if you didn't understand what that 10,340 means, apparently that means for length 10, perimeter is 340. but I couldn't understand it in my first read. so here goes the typical method of PS (:

x*y= 1600

y=1600/x

perimeter=  2* (x+y)

put y as 1600/x in the above equation:

perimeter=  2* (x+1600/x)

and plug in different values of x. Once you look at the option you actually don't have to calculate all. since there's no way the last three are going to give a lesser value for perimeter than will the first two (10 or 40) so just calculate for those two and you're done.

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Planning is in progress for a fenced, rectangular playground with an a

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