Question

The side of a square decreased by 20%. what percent its area will be decreased?

Answer 1

Let the side of square be a

Area = a^2

Side of new square formed = a - 20 % of a

= a - 20a/100

= a - a/5

= 4a/5

Area of new square = ( 4a/5)^2 = 16a^2 / 25

Decrease in Area = Original Area - New Area

= a^2 - 16a^2 /25

= 9a^2 / 25

Percentage of Increase = increase in Area × 100 / Original Area

= ( 9a^2 /25) × 100 / a^2

= 9a^2 × 4 / a^2

= 36 %

Answer 2

Let the side is x
Area = x^2
Now the side decreased by 20%
side = x-20%of x
       = 4x/5
Area = (4x/5)^2
Decrease in area = x^2 - (4x/5)^2
                            = 9x^2/25
Percentage decrease in area = (9x^2/25) x 100/x^2
                                               = 36%