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# What is the number of squares of perimeter 36 into which a rectangle

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
What is the number of squares of perimeter 36 into which a rectangle [#permalink]

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22 Sep 2017, 00:33
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25% (medium)

Question Stats:

81% (01:06) correct 19% (00:23) wrong based on 27 sessions

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What is the number of squares of perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned?

(A) 2
(B) 4
(C) 8
(D) 32
(E) 72

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Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: What is the number of squares of perimeter 36 into which a rectangle [#permalink]

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22 Sep 2017, 05:42
What is the number of squares of perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned?

Square perimeter = 36 => each side = 9
Rectangle measurement = 36 * 72

1st method ->
no. of square that will fit in length of rectangle = length of rectangle/ side of square = 72/9 =8
no. of square that will fit in breadth of rectangle = breadth of rectangle/ side of square = 36/9 =4

Total square = 8*4 = 32

2nd method
Area of square = 9*9 = 81
Area of rectangle = 36*72

No. of squares that can fit in rectangle = (36*72)/(9*9) = 32

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What is the number of squares of perimeter 36 into which a rectangle [#permalink]

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22 Sep 2017, 06:55
Bunuel wrote:
What is the number of squares of perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned?

(A) 2
(B) 4
(C) 8
(D) 32
(E) 72

Attachment:

squaresinrectangle.png [ 10.15 KiB | Viewed 632 times ]

To find the number of squares with perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned:

Squares with perimeter of 36 have side length 9

1. Sketch
---a rectangle with length 72 and width 36
---a few squares with side length 9 adjacent to one another, a few going across, a couple going down

It soon becomes evident (no need to draw the rest):
With 9 as each square's side length, 8 squares will fit inside the rectangle's length and 4 will fit inside its height, 8 * 4 = total 32

OR

2. Divide rectangle side lengths by square side lengths, then multiply what are essentially columns and rows

Rectangle length 72/9 = 8 squares on long side
Rectangle width 36/9 = 4 squares on short side
8 * 4 = 32 squares will fit into a partitioned rectangle

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What is the number of squares of perimeter 36 into which a rectangle   [#permalink] 22 Sep 2017, 06:55
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# What is the number of squares of perimeter 36 into which a rectangle

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