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%

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:

`(104)/(100)x=(26)/(25)x`

4. And the new short side is:

`(108)/(100)y=(27)/(25)y`

5. The new area is:

`((26)/(25)x)((27)/(25)y)=(702)/(625)xy`

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

`(702)/(625)xy-xy=0.1232xy`

7. The result is:

(0.1232)(100)=12.32%