Question

The ratio of the width to the length of a rectangle is 2:3, respectively. Answer each of the following. a 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

100%

Explanation:

do it yourself

Answer 2

The percentage increase in Area of rectangle is 200%

Explanation:

Given as :

The ratio of the width to the length of a rectangle is 2:3

Let The length of rectangle = 2 x

Let The width of rectangle = 3 x

∵ Area of rectangle = length × width

So,
`A_1` = 2 x × 3 x

Or,
`A_1` = 6 x²

Again

The increased length of rectangle = 2 x + 2 x = 4 x

The increase width of rectangle = 3 x + 50% of 3 x

I.e The increase width of rectangle = 3 x + 1.5 x = 4.5 x

∵ Increased Area of rectangle = increased length × increased width

Or,
`A_2` = 4 x × 4.5 x = 18 x²

So, The percentage increase in area =
`(A_2 - A_1)/(A_1)` × 100

Or, The percentage increase in area =
`(18 x^(2)-6x^(2))/(6x^(2))` × 100

Or , The percentage increase in area =
`(12)/(6)` × 100

∴ The percentage increase in area = 200

Hence, The percentage increase in Area of rectangle is 200% Answer