If the length of a rectangle is decreased by 10% and its width is decr

Question

If the length of a rectangle is decreased by 10% and its width is decreased by 20%, by what percent does its area decrease?

A. 30%
B. 28%
C. 25%
D. 23%
E. 15%

sj296 · Answer

Let's say length of the triangle = l 
breadth = b

area = l*b

=> After reducing the length by 10%, new length = 0.9*l
=> after reducing the breadth by 20%, new breadth = 0.8*b

=> new area = 0.72*l*b

=> % decrease =  \frac{(old - new)}{old} = \frac{((1-0.72)*100)}{1} = 28%

Option B

DashingNightmare2 · Answer

Area of rectangle = length * breadth
Area = l*b
New length =0.9 l
New breadth =0.8 b
New area = 0.9l *0.8 b = 0.72 l*b
hence its a 28% decrease 
Hence B

Catman · Answer

Let length and breadth be 10,10. 
Area of rectangle will be10*10= 100.
Now new sides will be length 9 and width 8.New area of the side is 72.
Thus the reduced area is 28.
28%.
Hence B.

Posted from my mobile device

BrentGMATPrepNow · Answer

STRATEGY: We have two different ways to solve this question:
Algebraic approach: Assign two variables to the length and width of the original rectangle, then calculate the new dimensions, etc
Assign easy-to-work-with values to the length and width.

Let's use the second approach (since it's easier)

Let 10 = the length of the original rectangle
Let 10 = the width of the original rectangle

Aside: Some students assert that these measurements are those of a square, not a rectangle. However, it's important to remember that a square is just a special kind of rectangle (in the same way that a square is a special kind of rhombus). So these measurements are perfectly fine.  
Area of the ORIGINAL rectangle = (base)(width) = (10)(10) =   100

The length of a rectangle is decreased by 10% and its width is decreased by 20%  
NEW length of the rectangle = 10 - (10% of 10) = 10 - 1 =   9  
NEW width of the rectangle = 10 - (20% of 10) = 10 - 2 =   8  
Area of the NEW rectangle = (base)(width) = (  9  )(  8  ) =   72

So, the area decreased from   100   to   72  
Percent decrease =  100(old - new)/old = (100)( 100  -  72 )/100 = (100)(28)/100 = 28%

Answer: B

If the length of a rectangle is decreased by 10% and its width is decr

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If the length of a rectangle is decreased by 10% and its width is decr

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