Question

if one side of rectangle is increased by 50 percent and other side decreased by 50 percent, the new area is how much percent less than the original area.

Answer 1

Answer:

25 % lesser

Step-by-step explanation:

let two sides be x ( length ) and y ( breadth )

area of rectangle = l * B

initial area = x * y = xy

let length x increase by 50%

new length = x + ( 50/100 ) * x

= x + ( 1/2 ) * x

= x + x/2

=2x/2 + x/2

= 3x/2 = new length

let breadth y decrease by 50%

new breadth = y - ( 50/100 ) * y

= y - ( 1/2 ) * y

= y - y/2

= 2y/2 - y/2

= y/2  = new breadth

new area = new length * new breadth

= 3x/2 * y/2

= 3xy/4

difference in areas = original area - new area =  xy - 3xy / 4

= 1/4 xy

percentage of decrease in areas  = ( difference of areas / initial area ) * 100

= ( 1/4xy  / xy ) * 100

= 1/4 * 100

= 25%

there fore new area is 25% lesser than original area