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# When a certain rectangle is divided in half, two squares are formed.

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Joined: 02 Sep 2009
Posts: 50572
When a certain rectangle is divided in half, two squares are formed.  [#permalink]

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20 Sep 2017, 21:51
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(N/A)

Question Stats:

95% (01:02) correct 5% (00:42) wrong based on 32 sessions

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When a certain rectangle is divided in half, two squares are formed. If each of these squares has perimeter 48, what is the perimeter of the original rectangle?

(A) 96
(B) 72
(C) 36
(D) 24
(E) 12

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Re: When a certain rectangle is divided in half, two squares are formed.  [#permalink]

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21 Sep 2017, 00:21
Bunuel wrote:
When a certain rectangle is divided in half, two squares are formed. If each of these squares has perimeter 48, what is the perimeter of the original rectangle?

(A) 96
(B) 72
(C) 36
(D) 24
(E) 12

Let each side of the square formed by dividing the rectangle be x.
Perimeter of the square = 4x=48
x=12
Perimeter of rectangle = 2(2x+x) =6x = 72

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Re: When a certain rectangle is divided in half, two squares are formed.  [#permalink]

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21 Sep 2017, 00:21
If the rectangle is divided into squares of perimeter 48, the side of the square is 12.

Since the rectangle is formed by adding two squares, the sides
of the rectangle are 24 and 12 respectively.

The perimeter of this rectangle is 2(length + breadth) = 2(24 + 12) = 72(Option B)

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When a certain rectangle is divided in half, two squares are formed.  [#permalink]

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21 Sep 2017, 12:59
Bunuel wrote:
When a certain rectangle is divided in half, two squares are formed. If each of these squares has perimeter 48, what is the perimeter of the original rectangle?

(A) 96
(B) 72
(C) 36
(D) 24
(E) 12

Instead of trying to deal with half a rectangle per the prompt, double a square.

Draw two connected squares to form a rectangle. Label each square's side "12."

See figure below (and visualize a vertical line down the middle, and on the right hand side, where both lines obviously equal 12).

At that point it is easy to see that the rectangle has two sides of 24 each and two sides of 12 each.

Perimeter of rectangle:

24 + 24 + 12 + 12 = 72

______12______|______12______|
|
|
12
|
|______12_____|______12______|
When a certain rectangle is divided in half, two squares are formed. &nbs [#permalink] 21 Sep 2017, 12:59
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