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

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Question 114473: the perimeter of a rectangle is 240cm . if the lenght is decreased .if the lenght is decreased by 10% and its breadth is increased by 20% we get the same perimeter. find the lenght and breadth of the rectangle
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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