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The area of a rectangle

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The area of a rectangle [#permalink] New post 08 Jan 2018, 13:20
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Question Stats:

78% (00:48) correct 21% (00:54) wrong based on 33 sessions



Quantity A
Quantity B
The area of a rectangle with a perimeter of 60 m
200 \(m^2\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudo for the right answer and explanation.
[Reveal] Spoiler: OA

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Re: The area of a rectangle [#permalink] New post 10 Jan 2018, 01:09
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So here we know that the rectangle has perimeter 60.
Since a rectangle can be a square we can maximize his area : 15*15 = 225
So QA is bigger.
However if we minimize we can say that one side equals = 1 and the other one = 29 which gives us 29.
So in this case it is bigger.

Is my reasoning correct?
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Re: The area of a rectangle [#permalink] New post 10 Jan 2018, 10:35
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Popo wrote:
So here we know that the rectangle has perimeter 60.
Since a rectangle can be a square we can maximize his area : 15*15 = 225
So QA is bigger.
However if we minimize we can say that one side equals = 1 and the other one = 29 which gives us 29.
So in this case it is bigger.

Is my reasoning correct?


Your reasoning is perfect.
I have edited the OP to show the correct answer is D

Cheers,
Brent
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Joined: 10 Apr 2015
Posts: 1228
Followers: 45

Kudos [?]: 1105 [0], given: 7

Re: The area of a rectangle [#permalink] New post 10 Jan 2018, 10:39
Expert's post
Carcass wrote:



Quantity A
Quantity B
The area of a rectangle with a perimeter of 60 m
\(200 m^2\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudo for the right answer and explanation.


Let's TEST some possible scenarios for Quantity A

Case 1:
If the perimeter is 60, then one possible scenario is that the base = 15 and the height = 15
In this case, the area = (15)(15) = 225
Here, Quantity A is greater

Case 2:
Another possible scenario is that the base = 25 and the height = 5 (perimeter still equals 60)
In this case, the area = (25)(5) = 125
Here, Quantity B is greater

Answer: D

Cheers,
Brent
_________________

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Re: The area of a rectangle   [#permalink] 10 Jan 2018, 10:39
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