Question

When the length of rectangular field is increased by 3m and breadth is reduced by 2m, its area gets decreased by 2m2. If the perimeter of the field is 56m then find how much percent of length should be reduced to make the field square.​

Answer 1

Answer:percentage reduce in length=25%

Explanation:

concept:

area of rectangle=l*b

perimeter of rectangle=2*(l+b)

Given: perimeter of rectangular field=56m

let length of rectangular field =x

let breadth of rectangular field =y

area of rectangular field=xy

perimeter of rectangular field=2(x+y)=56

x+y=28 ----->1

when length is increased by 3m and breadth is decreased by 2m, then area becomes

(x+3)(y-2)=xy-2 ----->2

from equation 1

(x+3)(28-x-2)=x(28-x)-2

(x+3)(26-x)=28x-x^2-2

23x-x^2+78=28x-x^2-2

5x=80

x=16

from equation 1

y=12

To make the field square length must be reduced by 4m

percentage reduce in length =4/16 *100

=25%

answer: percentage reduce in length=25%