BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Planning is in progress for a fenced, rectangular playground

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Planning is in progress for a fenced, rectangular playground

by BTGmoderatorLU » Thu Nov 15, 2018 3:21 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: Official Guide

Image

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

The OA is B
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Nov 15, 2018 10:10 pm
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
....
A 40 meter x 400 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
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu Nov 15, 2018 10:46 pm
BTGmoderatorLU wrote:Source: Official Guide

Image

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

The OA is B
Say the length of the playground is a meters and the breath is b meters.

Thus,

Area = ab = 1600 (given) and
Perimeter = 2(a + b)

We have to minimize the value of (a + b), given that ab = 1600 (constant)

Note that

If the product of two numbers is a constant, their sum would be minimum when the numbers are equal.

Thus, for (a + b) to be minimum, a = b. Thus, ab = 1600 => a^2 = 1600 => a = 40 meters.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Kukatpally | Hyderabad GMAT Prep | Bangalore GMAT Courses | Madhapur GRE Prep | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

Planning is in progress for a fenced, rectangular playground

by fskilnik@GMATH » Fri Nov 16, 2018 4:11 am
BTGmoderatorLU wrote:Source: Official Guide

Image

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
Reading Comprehension is part of the Quantitative Section of the GMAT:

Image

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri Nov 16, 2018 6:58 am
BTGmoderatorLU wrote:Source: Official Guide

Image

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
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Sun Mar 31, 2019 10:49 am
BTGmoderatorLU wrote:Source: Official Guide

Image

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

The OA is B
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1