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Squares and rectangles

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by vishubn » Mon Oct 20, 2008 8:07 pm
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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by aditi_bc » Mon Oct 20, 2008 8:41 pm
The entire object is a square so
3+3+3= 3+x+y (say the middle unnamed portion)
Thus y=6-x ------------------(1)

Now Sum of areas of SHADED = Sum of areas of UNSHADED

So, the equation will look like,
3*3+3*3+3y+3x+3x=3*3+3y+3y+3x

Solving the above will yield
y=3+x

Substitute value of 'Y' from equation (1)
6-x=3+x
=> x=3/2=1.5
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