# 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

1
by medhachuson7asidhu

2016-04-01T22:33:44+05:30
Perimeter of the given rectangle = 240cm
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.

there w