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The length of a rectangle is increased by 25% , but the width of the rectangle is decreased by 25%.  By what percent was the rectangle's area decreased?

 Jul 7, 2022
 #1
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The area is decreased by 4 percent.

 Jul 7, 2022
 #2
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The length of a rectangle is increased by 25% , but the width of the rectangle is decreased by 25%.  By what percent was the rectangle's area decreased?  

 

Let's do it with an example. 

 

Start with a rectangle that's 8 x 4.  The area of this rectangle is 32.  

 

8 + 25% = 10 

4 – 25% =   3                                  The area of this rectangle is 30

 

The area was decreased by 2

To get the percent of decrease, divide this by the size of the original rectangle. 

 

2/32 = 0.0625   so the percent of decrease is    6.25%   

 

This was a special case, using specific numbers. 

Try it with a few different size original rectangles, and see if the answer is consistently the same.  

.

 Jul 7, 2022
edited by Guest  Jul 7, 2022
 #3
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Here's another way: 

 

Let the width of the rectangle be \(w\), and let the length be \(l\)

 

The area of the original rectangle is \(w \times l\).

 

The area of the new rectangle is \(0.75w \times 1.25l = 0.9375 \times w \times l\).

 

This means that the area was decreased by \(1 - 0.9375 = \color{brown}\boxed{6.25 \text{%}}\)

 Jul 8, 2022

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