Question

The length of a rectangle is reduced by 22% and that of breadth is increased by 14%. Find the percentage change in area.​

Answer 1

Step-by-step explanation:

let the length of rectangle before change be $l$

let the breadth of rectangle before change be $b$

Area of rectangle before change = $lb$

Length of rectangle after change= $l - \frac{22l}{100} = \frac{78l}{100}$

Breadth of rectangle after change = $b + \frac{14b}{100} = \frac{114b}{100}$

Area of rectangle after change = $\frac{78l}{100} \times \frac{114b}{100} = \frac{8892lb}{10000}$

now percentage,

= $\frac{8892 \: \cancel{lb}}{100 \: \cancel{00}} \times \frac{1}{\cancel{lb}} \times 1\cancel{00} = 88.92\%$

now, percentage change in Area,

= $100\% - 88.92\%$ = $11.08\%$