Question

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

Answer 1

HEY DEAR ... ✌

_____________________________

UR QUESTION IS LITTLE BIT COMPLICATED .
HERE , WE GO ...

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

HOPE , IT HELPS ... ✌

Answer 2

refer the pic
hope it'll help
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