Question

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

Answer 1

The percent increase in area is 44%

Step-by-step explanation:

GIVEN

Length = 20 cm

Breadth = 15 cm

___________________________

We know that,

Area of rectangle = l × b

Area of rectangle = 20 × 15

Area of rectangle = 300

Area of rectangle = 300 cm

___________________________

If each side of the rectangle is increased by 20%

Length

percent = ( part / whole ) × 100

part = ( percent / 100 ) × whole

part = ( 20 / 100 ) × 20

part = 4

20% of 20 cm is 4 cm

20 + 4 = 24

If the side is increase by 20% then length will be 24cm

Breadth

part = ( percent / 100 ) × whole

part = ( 15 / 100 ) × 20

part = 3

20% of 15 cm is 3 cm

15 + 3 = 18

If the side is increase by 20% then breadth will be 18cm

___________________________

Now we have new length and new breadth

Let's find new area of rectangle

we know that,

Area of rectangle = l × b

Area of rectangle = 24 × 18

Area of rectangle = 432

Area of rectangle = 432 cm

___________________________

Now

Let's find the If each side of the rectangle is increased by 20% then the percent increase in area

432 - 300

= 132

The increase area is 132cm

Percent = ( part / whole ) × 100

Percent = ( 132 / 300 ) × 100

Percent = 44 × 100

Percent = 44

Percent = 44%

The percent increase in area is 44%

Answer 2

Given data:-

• The sides of a rectangle are 20 cm and 15 cm.
• each side of the rectangle is increased by 20%.

Here,

—› Length ( L ) = 20 cm

—› Breadth ( B ) = 15 cm

Solution:-

—› Area of old rectangle = L × B

—› Area of old rectangle = 20 × 15

—› Area of old rectangle = 300 cm²

To find area of new rectangle

• Each side of the rectangle is increased by 20%.

Let, x be the 20% of length 20 cm.

{we use percentage methode}

—› { x /20} × 100 = 20

—› { x /20} × 100 = 20

—› x/20 = 20/100

—› x/20 = 1/5

—› x = 1/5 × 20

—› x = 20/5

—› x = 4 cm .......( 1 )

Let, y be the 20% of breadth 15 cm.

{we use percentage methode}

—› { y /15} × 100 = 20

—› { y /15} × 100 = 20

—› y/15 = 20/100

—› y/15 = 1/5

—› y = 1/5 × 15

—› y = 15/5

—› y = 3 cm .......( 2 )

{ from eq. ( 1 ) & eq. ( 2 ) }

—› Length of new rectangle

= Length + x = 20 + 4 = 24 cm

—› Breadth of new rectangle

of new rectangle = Breadth + x = 15 + 3 = 18 cm

—› Area of new rectangle = L × B

—› Area of new rectangle = 24 × 18

—› Area of new rectangle = 432 cm²

To find change in area subtract area of given from rectangle area of new rectangle.

—› Change in area

= {Area of new rectangle} - {Area of old rectangle}

—› Change in area = {432} - {300}

—› Change in area = 132 cm²

To find the percentage of increase in the area:- Let, z be the increased percentage

—› z = {[Change in area×100]/Area of old rectangle}

—› z = {[132×100]/300}

—› z = 13200/300

—› z = 44%

Hence, the area of old rectangle increased by 44%.