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Area change for rectangle

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by mak_mak_mak » Mon May 31, 2010 11:17 pm
A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square then its area changes by :

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4
144
12
2
None of the above.
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by DeepthiRajan » Mon May 31, 2010 11:25 pm
Area of the rectangle = 14*10=140 cm^2

given that a new square is formed with sides: 14-x = 10+x

x= 4

area of the square = 12*12 = 144

hence area changes by 144-140=4---> (A)

HTH
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by Rahul@gurome » Mon May 31, 2010 11:27 pm
New length is 14-x and new width is 10+x.
Since the new figure is a square we have that 14-x = 10+x.
So 2x = 4
x = 2.
So new length is 12 and new area is 12^2 = 144.
initial area is 14*10 = 140.
So area is changing by 144-140 = 4.
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by mak_mak_mak » Mon May 31, 2010 11:28 pm
DeepthiRajan wrote:Area of the rectangle = 14*10=140 cm^2

given that a new square is formed with sides: 14-x = 10+x

x= 4

area of the square = 12*12 = 144

hence area changes by 144-140=4---> (A)

HTH
Thanks Deepthi, I misread the question and thereby learnt a lesson, not to rush :)
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by selango » Mon May 31, 2010 11:29 pm
Let l=14 and w =10

Area of rectangle=14*10=140

l is decreased by x cms and w is increased by x cms to form a square

So (14-x) and (10+x) are the sides of square and equal

14-x=10+x

2x=4-->x=2

So area of the square=12*12=144

So the area changes by 4

Answer 4
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by 4GMAT_Mumbai » Mon May 31, 2010 11:29 pm
The rectangle becomes a square when length = breadth.

i.e., 14 - x = 10 + x

x = 12.

Area of the new square = 12 times 12 = 144

Area of the old rectangle = 14 times 10 = 140

Hence, the area increases by 4 units.

Corollary (food for munching ...) : If the perimeter of the rectangle has to be a constant, the area is maximum when the rectangle becomes a square.

Hope this helps. Thanks.
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