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# A piece of wire used to fence a rectangular land can be used to fence

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Manager
Joined: 15 Dec 2015
Posts: 120
GMAT 1: 660 Q46 V35
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WE: Information Technology (Computer Software)
A piece of wire used to fence a rectangular land can be used to fence [#permalink]

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01 Aug 2017, 01:43
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A piece of wire used to fence a rectangular land can be used to fence a square land that has twice the width of the rectangular land.What is the area of the square land if the area of the rectangular land is 100 sq units less than the area of the square land?

A. 100 sq units
B. 300 sq units
C. 400 sq units
D. 900 sq units
E. 1000 sq units
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5660
Re: A piece of wire used to fence a rectangular land can be used to fence [#permalink]

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01 Aug 2017, 01:56
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KUDOS
Expert's post
DH99 wrote:
A piece of wire used to fence a rectangular land can be used to fence a square land that has twice the width of the rectangular land.What is the area of the square land if the area of the rectangular land is 100 sq units less than the area of the square land?

A. 100 sq units
B. 300 sq units
C. 400 sq units
D. 900 sq units
E. 1000 sq units

Hi..
rectangular field -$$2*( l+b)$$
square= $$(2b)*4=8b$$....
so $$2l+2b=8b.....l=3b$$....

also $$(2b)^2-l*b=100.....4b^2-3b*b=100.....b^2=100....b=10$$

so area of rectangle = $$(2*10)^2=400$$

C
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A piece of wire used to fence a rectangular land can be used to fence [#permalink]

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01 Aug 2017, 02:39
1
KUDOS
Given data:
Length or wire needed to fence both the rectangle and the square is the same.
The side of the square is twice the width of the rectangle.
Area(Square) - Area(Rectangle) = 100

We have been asked to find the area of the square

Let the length and width of the rectangle be y and x.
From the question stem, side of square is 2x
$$2(y+x) = 4(2x)$$
Therefore, $$y = 4x-x =3x$$

We know that Area(Square) - Area(Rectangle) = 100
Therefore $$4x^2 - x(3x) = 100 => x^2 = 100 => x = 10$$(because side cannot be negative)
Hence, area of square is $$(2x)^2 = 20^2 = 400$$(Option C)
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A piece of wire used to fence a rectangular land can be used to fence   [#permalink] 01 Aug 2017, 02:39
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