The figure above represents a square garden that is divided

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The figure above represents a square garden that is divided [#permalink]

15 Sep 2007, 16:20

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The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?

A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5

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15 Sep 2007, 16:51

areas of shaded region
3*3+3*3+(6-x)3+3*x+3*x=36+3x

the area of unshaded region
3*3+(6-x)3+(6-x)3+3*x=45-3x

now S1=S2

36+3x=45-3x
6x=9
x=1.5

C

Last edited by Ravshonbek on 15 Sep 2007, 16:52, edited 1 time in total.

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15 Sep 2007, 16:51

shaded regions = (9-3-x)*3+3*3+3*3+3x+3x = 18-3x+18+6x

unshaded regions = (9-3-x)*3+(9-3-x)*3+3*3+3x = 18-3x+18-3x+9+3x

since:

shaded regions = unshaded regions

18-3x+18+6x = 18-3x+18-3x+9+3x

36+3x = 36-6x+9+3x

9 = 6x

x = 1.5

the answer is (C)

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16 Sep 2007, 08:55

nice works..now why didnt i think of solving it this way??

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16 Sep 2007, 11:46

OA is indeed C.

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16 Sep 2007, 18:30

Key is "square garden". :-)

- Brajesh

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16 Sep 2007, 23:08

Ans :C.

Attachment is my working.

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16 Sep 2007, 23:23

ywilfred wrote:

Ans :C.

Attachment is my working.

Nice work !

[#permalink] 16 Sep 2007, 23:23

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The figure above represents a square garden that is divided

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The figure above represents a square garden that is divided

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