# The perimeter of a rectangle is 240cm. If it's 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

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let the length of the the rectangle be = x cm

let the breadth of the rectangle be = y cm

A/Q

2( x + y ) =240

or x + y + 120 ------------(1) [ divided both sides by 2]

now,

let the new length be = x - 10/100 x [ since the length is decreased

by 10% ]

= (100x - 10x) 100 = 90/100x = 9/10x

let the new breadth be = y + 20/100y [ since the breadth is increased

by 20%]

= (100y = 20y)100 + 120/100y +12/10y

now, A/Q

2( 9/10x +12/10y) =240

or 9/10x + 12/10 = 120 ------------(2) [ divided both sides by 2]

from equation (1) and (2)

x+y = 9/10x + 12/10y

or 10(x +y) = 9x +12y [multiplied both sides by 10]

or 10x + 10y = 9x + 12y

or 10x - 9x = 12y - 10y

or x = 2y

or x - 2y = 0 --------------(3)

subtracting equation (3) from (1)

x + y - (x - 2y) = 120 - 0

or x + y -x + 2y = 120

or 3y = 120

or y = 120/3 = 40

so the breadth of the 1st rectangle is 40cm.

putting the value of y in equation (1) ---

x + y = 120

or x + 40 = 120

or x = 120 - 40 = 80

so the length of the 1st rectangle is 80cm.

now,

length of the 2nd rectangle = 9/10x = 9/10 x 80 = 72

breadth of te 2nd rectangle = 12/10y = 12/10 x 40 = 48

therefore, the length and breadth of the 1st rectangle is 80cm and 40cm respectively and the length and breadth of the 2nd rectangle is 72cm and 48cm respectively.