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# A flat, rectangular flower bed with an area of 2,400 square

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Joined: 07 Jun 2014
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A flat, rectangular flower bed with an area of 2,400 square [#permalink]  05 Jun 2016, 12:32
Expert's post
00:00

Question Stats:

21% (00:06) correct 78% (03:07) wrong based on 14 sessions
A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the fourth side. If the entire length of the fence is 140 feet, which of the following could be the length, in feet, of one of the sides of the flower bed?

Indicate all such lengths.

A. 20
B. 30
C. 40
D. 50
E. 60
F. 70
G. 80
H. 90

[Reveal] Spoiler: OA
B, C, E, and G

Practice Questions
Question: 11
Page: 102 - 103
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: A flat, rectangular flower bed with an area of 2,400 square [#permalink]  05 Jun 2016, 12:39
Expert's post
Explanation

You know that the area of the rectangular flower bed is 2,400 square feet. So if the flower bed is a feet long and b feet wide, then ab = 2,400. If the side of the flower bed that is bordered by the walkway is one of the sides that are b feet long, then the total length of the three sides of the flower bed bordered by the fence is 2a + b feet. Since you are given that the total length of the
fence is 140 feet, it follows that 2a + b = 140. Since ab = 2,400, you can substitute $$\frac{2400}{a}$$ for b
in the equation 2a + b = 140 to get the equation $$2a + \frac{2400}{a}=140$$. It follows that $$2a^2 + 2400 = 140a$$, or $$a^2 - 70a + 1200 = 0$$.

When you solve this equation for a (either by factoring or by using the quadratic formula), you get a = 30 or a = 40. If a = 30, then
$$b = \frac{2400}{30} =80$$; if a = 40, then $$b = \frac{2400}{40} =60$$. So the possible lengths of the sides are 30, 40, 60, and 80. Thus the correct answer consists of Choices B, C, E, and G.
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Sandy
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Re: A flat, rectangular flower bed with an area of 2,400 square [#permalink]  06 Apr 2017, 03:59
Hi, new from Australia and why not the answer is not F for bedding question?
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Shopping of different sizes of bed heads aushoppinghub com/product-category/bed-heads/ online in Australia.

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: A flat, rectangular flower bed with an area of 2,400 square [#permalink]  06 Apr 2017, 07:24
Expert's post
RobCons wrote:
Hi, new from Australia and why not the answer is not F for bedding question?

Because you do not have a side equal to 70 in this case. Sides are either 30, 80 or 40, 60
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Re: A flat, rectangular flower bed with an area of 2,400 square   [#permalink] 06 Apr 2017, 07:24
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