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

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Bunuel
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If the length of a rectangle is decreased by 10% and its width is decr [#permalink] New post   31 Aug 2021, 03:02
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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%
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B
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sj296
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If the length of a rectangle is decreased by 10% and its width is decr [#permalink] New post   Updated on: 31 Aug 2021, 03:07
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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

Originally posted by sj296 on 31 Aug 2021, 03:07.
Last edited by sj296 on 31 Aug 2021, 03:07, edited 1 time in total.
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Re: If the length of a rectangle is decreased by 10% and its width is decr [#permalink] New post   31 Aug 2021, 03:07
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
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Re: If the length of a rectangle is decreased by 10% and its width is decr [#permalink] New post   31 Aug 2021, 07:15
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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.

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Re: If the length of a rectangle is decreased by 10% and its width is decr [#permalink] New post   28 Mar 2022, 12:22
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Bunuel wrote:
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%


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
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Re: If the length of a rectangle is decreased by 10% and its width is decr [#permalink]
28 Mar 2022, 12:22
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