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

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What is the % change in the area of a rectangle when its len [#permalink] New post   06 Oct 2010, 06:09
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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
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D
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Re: What is the % change in the area of a rectangle...... [#permalink] New post   06 Oct 2010, 06:24
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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.

Answer: D.
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Re: What is the % change in the area of a rectangle...... [#permalink] New post   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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Re: What is the % change in the area of a rectangle...... [#permalink] New post   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] New post   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
Answer D....

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Re: What is the % change in the area of a rectangle when its len [#permalink] New post   13 Jul 2018, 14:23
Expert Reply
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.

Answer: D
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Re: What is the % change in the area of a rectangle when its len [#permalink] New post   27 Feb 2021, 11:48
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

\(+10 - 10 + \frac{(-10)(+10)}{100} = -1\), Answer must be (D)
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What is the % change in the area of a rectangle when its len [#permalink] New post   28 Feb 2021, 07:53
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To find

    • % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%.

Approach

Let’s assume, length of the rectangle = l and width = w
    • Area = l × w
New length = l+ 0.1 l = 1.1 l
New width = w - 0.1 w = 0.9 w
    • New area = 1.1 l × 0.9 w = 0.99 (l × w)
Decrease = l × w - 0.99 (l × w) = 0.01 (l × w)
    • Percentage decrease = \(\frac{0.01(l × w) }{ (l × w)}\) × 100 = 1%

Hence, the correct answer is option D.
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Re: What is the % change in the area of a rectangle when its len [#permalink] New post   04 Mar 2022, 04:38
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