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Fence for rectangle and square


spoud74

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One person has a fence, and he uses the fence for a rectangle area, and the length is twice longer than the width. if he uses the fence for a square, the area will be 400 feet bigger. how long is the fence?

1). 16

2). 40

3). 160

4). 1200

5). 1600

 

Rectangle width = x

Rectangle length = 2x

Rectangle perimeter = 2(x+2x) = 6x

If legth of 6x is to be used for a square then each side of the sqare will be of length 6x/4 = 3x/2

 

Area of Square = (3x/2)^2

Area of rectanlge = 2x^2

 

(9/4)x^2 - 2x^2 = 400

(1/4)x^2=400

x=40

Length of fence = 6(40) = 240 :doh: Not one of the answer choices. I am not sure where I went wrong in my assumptions.

 

Would appreciate a double check.

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I think both the highlighted portions don't match!

length = 3x!

 

One person has a fence, and he uses the fence for a rectangle area, and the length is twice longer than the width. if he uses the fence for a square, the area will be 400 feet bigger. how long is the fence?

1). 16

2). 40

3). 160

4). 1200

5). 1600

 

Rectangle width = x

Rectangle length = 2x

Rectangle perimeter = 2(x+2x) = 6x

If legth of 6x is to be used for a square then each side of the sqare will be of length 6x/4 = 3x/2

 

Area of Square = (3x/2)^2

Area of rectanlge = 2x^2

 

(9/4)x^2 - 2x^2 = 400

(1/4)x^2=400

x=40

Length of fence = 6(40) = 240 :doh: Not one of the answer choices. I am not sure where I went wrong in my assumptions.

 

Would appreciate a double check.

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ravindra_iit, if I suppose that rectangle length = 3x, then solving for the perimeter, I get 160 which is one of the answer choices.

 

I am having trouble though translating the question to the point which says:

l = 3x

w = x

 

To me it sounds like the question is saying

l = 2x

w = x

 

Anyone else care to provide an opinion?

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