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# What is the % change in the area of a rectangle when its len

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Manager
Joined: 22 Sep 2010
Posts: 84
What is the % change in the area of a rectangle when its len  [#permalink]

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06 Oct 2010, 06:09
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Difficulty:

15% (low)

Question Stats:

82% (00:46) correct 18% (00:54) wrong based on 96 sessions

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What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data
Math Expert
Joined: 02 Sep 2009
Posts: 49276
Re: What is the % change in the area of a rectangle......  [#permalink]

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06 Oct 2010, 06:24
pzazz12 wrote:
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data

General formula for percent increase or decrease, (percent change):

$$Percent \ change=\frac{Change}{Original}*100$$.

$$area_{original}=lw$$ and $$area_{new}=1.1l*0.9w=0.99lw$$ --> $$Percent \ change=\frac{Change}{Original}*100=\frac{lw-0.99lw}{lw}*100=1%$$ decrease.

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Joined: 12 Oct 2010
Posts: 14
Re: What is the % change in the area of a rectangle......  [#permalink]

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12 Oct 2010, 13:16
Substitute if you don't know the formula.

First "rectangle" can be 10x10 so area is 100
Increase length by 10% and decrease width by 10% so 11x9 area is 99

100-99=1 sqft

1sqft is a 1% change from a 100 sqft rectangle.
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Joined: 24 Jun 2010
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Re: What is the % change in the area of a rectangle......  [#permalink]

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12 Oct 2010, 14:55
(11/10)*(9/10) = 99/100 of original area

99/100 is a 1% decrease from 100/100 ->D
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Re: What is the % change in the area of a rectangle when its len  [#permalink]

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18 May 2017, 12:56
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?
A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data

Let Length be = 2
Let width be = 1
Area of rectangle = Length x width = 2 x 1 = 2
Length increases by 10% = 110% of 2 = $$\frac{110}{100}$$ x 2 = 2.2
Width decreases by 10% = 90% of 1 = $$\frac{90}{100}$$ x 1 = 0.9
New area of rectangle = 2.2 x 0.9 = 1.98

Change in Area = 2 - 1.98 = 0.02

Percentage Change = Change in Area / Initial Area x 100
Percentage Change = $$\frac{0.02}{2}$$ x 100 = 1% decrease

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Re: What is the % change in the area of a rectangle when its len  [#permalink]

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13 Jul 2018, 14:23
pzazz12 wrote:
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data

We can let L = the original length and W = the original width of the rectangle. Thus, the area of the original rectangle is LW and the area of the new rectangle is 1.1L x 0.9W = 0.99LW. We see that the area of the new rectangle is 1% less than the area of the original rectangle.

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Re: What is the % change in the area of a rectangle when its len &nbs [#permalink] 13 Jul 2018, 14:23
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