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# Percent

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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