Question

The sides of a rectangle are 20cm and 15cm. If each side of the rectangle is increased by 20%, find the percentage increase in the area?

Answer 1

The percentage of increase in the area = 44%

Given :

• The sides of a rectangle are 20 cm and 15 cm.

• Each side of the rectangle is increased by 20%

To find :

The percentage of increase in the area

Solution :

Step 1 of 4 :

Find area of the original rectangle

The sides of the rectangle are 20 cm and 15 cm

The area of the rectangle

= 20 cm × 15 cm

= 300 cm²

Step 2 of 4 :

Find the new sides of the rectangle

Each side of the rectangle is increased by 20%

Length of the rectangle

$\displaystyle \sf{ = 20 \times \frac{120}{100} \: \: cm }$

$\displaystyle \sf{ = 24 \: \: cm }$

Breadth of the rectangle

$\displaystyle \sf{ = 15 \times \frac{120}{100} \: \: cm }$

$\displaystyle \sf{ = 18 \: \: cm }$

Step 3 of 4 :

Find area of the new rectangle

The area of the new rectangle

= 24 cm × 18 cm

= 432 cm²

Step 4 of 4 :

Find percentage of increase in the area

The increase in the area

= 432 cm² - 300 cm²

= 132 cm²

The percentage of increase in the area

$\displaystyle \sf{ = \frac{132}{300} \times 100\%}$

$\displaystyle \sf{ = \frac{132}{3} \%}$

$\displaystyle \sf{ = 44 \: \%}$