Question

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

Answer 1

Answer:

perimeter of rectangle is 240.

let length and breadth would be l & b respectively.

perimeter of rectangle : 2 ( l + b) = 240

2l + 2b = 240...... (1)

according to statement,

then new length : l * 90/100 & breadth : b * 120/100

formula of perimeter of rectangle :

2 ( length + breadth) = 2 ( l * 90 /100 + b * 120/100) = 240

2 ( 90 l + 120b /100 ) = 240

180l + 240b = 240 * 100 = 24000.......(2)

we will multiply 1st equation by 90.

90(2 l + 2b ) = 90(240)

180l + 180b = 21600 .... (3)

subtract ( 3) equation from ( 2 )

180l + 240b = 24000 .... ( 2 )

180l + 180 b = 21600 ... ( 3 )

- - -

60b = 2400

b = 2400 /60 = 40 CM

put value of b in 1st equation.

2l + 2b = 240

2l + 2 ( 40 ) = 240 2l = 160 l = 160/2 = 80cm

so, length = 80cm & breadth 40cm