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In a certain housing development, each garden has the shape

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In a certain housing development, each garden has the shape  [#permalink]

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New post 28 Nov 2016, 11:18
2
2
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A
B
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D
E

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Question Stats:

82% (02:20) correct 18% (02:25) wrong based on 216 sessions

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In a certain housing development, each garden has the shape of a rectangle whose width is 2/3 its length and the length of the largest garden in the development is 2 times the length of the smallest garden in the development. If the perimeter of the smallest garden is 30 feet, what is the area of the largest garden?

A) 45
B) 54
C) 81
D) 108
E) 216


How can we solve this problem?

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Re: In a certain housing development, each garden has the shape  [#permalink]

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New post 02 Dec 2016, 06:47
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3
HarveyKlaus wrote:
In a certain housing development, each garden has the shape of a rectangle whose width is 2/3 its length and the length of the largest garden in the development is 2 times the length of the smallest garden in the development. If the perimeter of the smallest garden is 30 feet, what is the area of the largest garden?

A) 45
B) 54
C) 81
D) 108
E) 216


We are given that the length of the largest garden in the development is 2 times the length of the smallest garden in the development. If we let the length of the smallest garden = S, then we can let the length of the largest garden = 2S.

We are also given that the perimeter of the smallest garden is 30 feet. Since the width is 2/3 the length, the width = (2/3)S. Thus, we can create the following equation:

2S + 2(2/3)S = 30

2S +(4/3)S = 30

Multiplying the entire equation by 3 gives us:

6S + 4S = 90

10S = 90

S = 9

Thus, the length of the largest garden is 2 x 9 = 18, and the width of the largest garden is (2/3) x 18 = 12.

Therefore the area of the largest garden is 18 x 12 = 216.

Answer: E
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Re: In a certain housing development, each garden has the shape  [#permalink]

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New post 28 Nov 2016, 11:33
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Width = 2/3*Length

Largest Length = 2* Smallest length

Smallest perimeter = 30=> 2*(Smallest_length+2/3*smallest_length)...solving we have smallest length = 9

Therefore Largest_length = 18 => largest_width = 2/3*18 = 12

Therefore largest area = 18*12 = 216

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Re: In a certain housing development, each garden has the shape  [#permalink]

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New post 19 Feb 2018, 04:46
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Re: In a certain housing development, each garden has the shape   [#permalink] 19 Feb 2018, 04:46
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