Question

The 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 the original length and breadth of the rectangle .

Answer 1

Convert the new dimensions to: .9L and 1.2B
:
2L + 2b = 240
Simplify, divide by 2:
L + B = 120
L = 120-B; use for substitution
:
New dimensions
2(.9L) + 2(1.2B) = 240
Simplify divide by 2:
.9L + 1.2B = 120
:
Substitute (120-B) in the above equation

.9(120-B) + 1.2B = 120
108 - .9B + 1.2B = 120
.3B = 120 - 108
.3B = 12
B = 12/.3
B = 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


length = 80
breath =40

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Answer 2

Please view the answer below. Hope it helps