Question

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.)

Answer 1

Answer: 12.32%

Step-by-step explanation:

1. $x$ is the original long side and $y$ is the original short side.

2. The area of the original rectangle is $xy$.

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

$\frac{104}{100}x=\frac{26}{25}x$

4. And the new short side is:

$\frac{108}{100}y=\frac{27}{25}y$

5. The new area is:

$(\frac{26}{25}x)(\frac{27}{25}y)=\frac{702}{625}xy$

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

$\frac{702}{625}xy-xy=0.1232xy$

7. The result is:

(0.1232)(100)=12.32%