Question

The ratio of the width to the length of a rectangle is 2:3, respectively. Answer each of the following. By what percent would the area of the rectangle change if the width of the rectangle is increased by 50% and the length is increased by the same number of units?

Answer 1

The area of rectangle is increased by 200%

Explanation:

Given the ratio of the width to the length of a rectangle is 2:3, respectively.

∴ Width = 2x units

and Length = 3x units

`Area = Width * length`

=
`2x* 3x=6x^2` square units

now, if the width of the rectangle is increased by 50% and the length is increased by the same number of units

then width and length becomes

New width=2x+0.05(2x)=2x+x=3x units

and length=3x+3x=6x units

Therefore,
`New area=Width* length`

=
`3x* 6x=18x^2` square units

Area increased by percentage =
`(New Area-Old Area)/(Old Area)* 100`

=
`(18x^(2)-6x^(2))/(6x^(2)) * 100=(12x^(2) )/(6x^(2)) * 100`

= 200%