Question

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

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
I hope this helps you.