Question

9 All the side of a rectangle is increased by 20%, find the % increased in area.
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Answer 1

Step-by-step explanation:

Given:-

All the sides of a rectangle is increased by 20%

To find:-

Find the % increased in area ?

Solution:-

Let the length of the rectangle be l units

Let the breadth of the rectangle be b units

Area of the rectangle = lb sq.units

Let the length is increased by 20% then the new length will be

=> l +20% of l

=> l+(20% × l)

=> l+(20/100)×l

=>l +(1/5) l

=> l +( l/5)

=> (5l +l)/5

=> 6l/5 units

Let the breadth is increased by 20% then the new breadth will be

=> b +20% of b

=> b+(20% × b)

=> b+(20/100)×b

=>b +(1/5)× b

=> b +( b/5)

=> (5b+b)/5

=> 6b/5 units

Area of the rectangle

=> (6l/5)×(6b/5) sq.units

=>(6l×6b)/(5×5)

=> 36lb/25

=> (36/25) lb sq.units

Area of the original rectangle = lb sq.units

Area of the new rectangle = (36/25) lb units

Increasing in the Area

=> New area - Original area

=> (36/25)lb -lb

=>[ (36/25)-1] lb

=>[ (36-25)/25 ] lb

=> (11/25)lb sq.units

Now

Increasing percentage in the area

=>( Increasing in the area/Original area)×100

=>[[ (11/25)lb]/lb]×100

=> (11/25)×100

=> (11×100)/25

=> 11×4

=> 44 %

Shortcut:-

If the length and the breadth is increased by X% then the increasing percentage in the area is

2X+(X^2/100)%

=> (2×20)+(20×20)/100

=> 40+(400/100)

=> 40+4

=> 44%

Answer:-

The increasing percentage in the area is 44%

Used formula:-

• Area of a rectangle = lb sq.units

• l = length

• b= breadth