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A rectangular garden is extended 4% on the long sides and 8% on the short sides. To the nearest hundredth of a percent, by what percent does the area of the rectangle increase? (Hint: Let x = the length of the original long side and y = the length of the original short side. Multiple the new side lengths and compare to x*y which is the area of the original rectangle.)

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Answer: 12.32%

Step-by-step explanation:

1. [tex]x[/tex] is the original long side and [tex]y[/tex] is the original short side.

2. The area of the original rectangle is [tex]xy[/tex].

3. The rectangle is extended 4% on the long sides and 8% on the short sides. therefore, the new long side is:

[tex]\frac{104}{100}x=\frac{26}{25}x[/tex]

4. And the new short side is:

[tex]\frac{108}{100}y=\frac{27}{25}y[/tex]

5. The new area is:

[tex](\frac{26}{25}x)(\frac{27}{25}y)=\frac{702}{625}xy[/tex]

6. The percentage of increase is calculated by substracting the new area and the original area:

[tex]\frac{702}{625}xy-xy=0.1232xy[/tex]

7. The result is:

(0.1232)(100)=12.32%

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