Question

the sum of length and breadth of a rectangle is 240 CM if the length is discarded by 20% and the breadth is increased by 10% perimeter of remaining same find in deamination of the rectangle

Answer 1

Let the dimensions of the

 

rectangle are

 

i) length = x cm

 

breadth = y cm

 

Perimeter = 240 cm ( given )

 

2( x + y ) = 240

 

x + y = 120 ----( 1 )

 

If length is decreased by 10% and

 

breadth is increased by 20% then

 

the new dimensions are

 

Length = x ( 100-10)/100

 

= 90x /100

 

= 9x /10

 

Breadth = y× ( 100 +20 )/100

 

= 120y /100

 

= 12y /10

 

Perimeter = 240 cm

 

2 [ 9x /10 + 12y /10 ] = 240

 

9x + 12y = 1200

 

Divide each term with 3

 

3x + 4y = 400-----( 2 )

 

Multiply equation ( 1 ) with 3 and

 

Subtract from ( 2 )

 

y = 40

 

Put y = 40 in ( 1 )

 

x = 80

 

 

Therefore ,

 

Required rectangle dimensions are

 

Length = x = 80 cm

 

Breadth = y = 40 cm

 

There’s an alternate method too:

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

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

        ⇒         10x + 10y = 9x + 12y

        ⇒         10x - 9x = 12y - 10y

        ⇒                x = 2y

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

 

                      subtracting equation (3) from (1)

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

       ⇒  x + y -x + 2y = 120

       ⇒                  3y = 120

       ⇒                   y  = 120/3 = 40

 

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

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

                           x + y = 120

                 ⇒  x + 40 = 120

                 ⇒         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 This Helps :)