Question

If the length of a rectangle is increased by 120%, and its width is decreased by 20%, what is the percentage change in the area of the rectangle? (rea=length*width)

Answer 1

The area of the rectangle is increased in 76 percent.

Explanation:

The area of a rectangle (
`A`) is represented by the following formula:

`A = w\cdot l`

Where:

`w` - Width.

`l` - Length.

If length is increased by 120 %and width is decreased by 20 %, the percentage change in the area of the rectangle is: (
`l = 2.2\cdot l_(o)`,
`w = 0.8\cdot w_(o)`)

`A = (2.2\cdot l_(o))\cdot (0.8\cdot w_(o))`

`A = (2.2)\cdot (0.8)\cdot w_(o)\cdot l_(o)`

`A = 1.76\cdot A_(o)`

The area of the rectangle is increased in 76 percent.