Question

if the length of a rectangle is increased by 30 percentage and the width of the same rectangle is decreased by 30 what is the affect on the area

Answer 1

The area will decrease by 9%.

Explanation:

The area of a rectange is given by the formula below.

`\boxed{\text{Area of rectangle}= \text{length}×\text{width}}`

Let the original length and width of the rectangle be L and W respectively.

Start by finding the original area:

Original dimensions

Length= L= 100%L

Width= W= 100%W

Original area= LW

Let's find the dimensions of the new rectangle in terms of L and W.

New dimensions

Length= (100% +30%)L= 130%L

Width= (100%-30%)W= 70%W

New area

`= (130)/(100) L * (70)/(100) W`

`= (91)/(100) LW`

= 91% LW

Comparing the new area with the original area:

100% LW- 91% LW= 9% LW

∴ The area will decrease by 9%.

*Note that percentage is equivalent to dividing a number by 100.