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Planning is in progress for a fenced, rectangular playground

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

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Source: Official Guide

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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
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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

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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
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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:

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

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