The perimeter of a rectangle is 240 m if its length is decreased by 10% and breadth is increased by 20% , we get the same perimeter, find the length and the breadth of the both the rectangles.

Perimeter of a rectangle
2L + 2W = 240
Simplify,  by 2:

L + W = 120
L = 120-W; use for substitution

 length is decreased by 10% and breadth is increased by 20% 
new dimensions
 let the new length be =L - 10/100 L 
                                     = (100L - 10L) 100 = 90/100L= 9/10L

   let the new breadth be = W + 20/100W 
                                       = (100W  + 20W)100 = 120/100 W =12/10W

THE PERIMETER = 2L+2W =240
2(9/10L) + 2(12/10W) = 240   divided by 2 

9/10L +12/10W = 120

fiirst equation   L + W = 120
second equation   9/10L +12/10W = 120

so    L + W   = 9/10L +12/10W 
 
THE FIRST RECTANGLE 

so  L = 80
W = 40 

THE SECOND 
L= 72cm and W= 48cm r

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