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A rectangular region has a fence along three sides and a

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TOUGH GUY
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A rectangular region has a fence along three sides and a [#permalink] New post   Updated on: 26 Jun 2013, 02:34
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A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet?

A. 4
B. 8
C. 16
D. 32
E. 64
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D

Originally posted by TOUGH GUY on 08 Oct 2006, 10:01.
Last edited by Bunuel on 26 Jun 2013, 02:34, edited 1 time in total.
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[#permalink] New post   08 Oct 2006, 10:08
A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet?

A. 4 B. 8 C. 16 D. 32 E. 64
two sides EACH = x the third = 2x and the wall length is thus 2x too

x*2x = 2x^2 = 128 ie x^2 = 64 ie x = 8

L = 16 W=8

TOTAL LENGHT OF FENCE = 2*8+16 = 32

MY ANSWER IS D
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[#permalink] New post   08 Oct 2006, 13:21
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32

2x * x = 128
2x^2 = 128
x^2 = 64
x = 8

perimeter = 2x + x + x = 4x = 4(8) = 32
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[#permalink] New post   08 Oct 2006, 23:57
x = 2y
x * y = 128
2y^2 = 128
y = 8
x = 16

fence = y + y + x = 32
D
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A rectangular region has a fence along three sides and a [#permalink] New post   26 Jun 2013, 02:37
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A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet?
A. 4
B. 8
C. 16
D. 32
E. 64

The fenced side opposite the wall = 2x.
Each of the other two fenced sides = x.

The area = 2x*x=128 --> x=8.

The total length of the fence = x + x + 2x = 4x = 32 feet.

Answer: D.

Hope it's clear.
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Re: A rectangular region has a fence along three sides and a [#permalink] New post   14 Oct 2013, 01:32
Please refer the screenshot attached:

2x ^ 2 = 128
x = 8

4x = Perimeter of fence = 32 (Answer = D)
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wall.JPG
wall.JPG [ 5.57 KiB | Viewed 13608 times ]

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Re: A rectangular region has a fence along three sides and a [#permalink] New post   12 Dec 2021, 08:15
Rectangular with side a, b, longer side a, shorter side b.
The fenced side opposite the wall is twice the length of each of the other two fenced sides
=> Interpret it as a =2b.
a= 2b, axb = 128 ==> 2b^2 =128 ==> b =8.
=> Total length of the fence = a+2b = 2b+2b = 4b = 8x4 =32.
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Re: A rectangular region has a fence along three sides and a [#permalink]
12 Dec 2021, 08:15
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