Question

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

Answer 1

The perimeter of a rectangle is 240cm. If the length is decreased by 10% and it's breadth is increased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
:
Convert the new dimensions to: .9L and 1.2W
:
2L + 2W = 240
Simplify, divide by 2:
L + W = 120
L = 120-W; use for substitution
:
New dimensions
2(.9L) + 2(1.2W) = 240
Simplify divide by 2:
.9L + 1.2W = 120
:
Substitute (120-W) in the above equation:
.9(120-W) + 1.2W = 120
108 - .9W + 1.2W = 120
.3W = 120 - 108
.3W = 12
W = 12/.3
W = 40
:
Find L
L = 120 - 40
L = 80
:
Check solution:
2(80) + 2(40) = 240
and
2(.9*80) + 2(1.2*40) = 
144 + 96 = 240