SOLUTION: the perimeter of a rectangular garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % , we get the same perimeter. then the length and breadth of th

Question 1102530: the perimeter of a rectangular garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % , we get the same perimeter. then the length and breadth of the new formed rectangular garden , respectively are
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

System should be

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,

--------The following work and results are wrong-----------

------------length of the ORIGINAL garden
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-----------width of the ORIGINAL garden
Question asks for the new garden; not for the original garden.
NEW garden dimensions:

-

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
the perimeter of a rectangular garden is 420 cm . If its length is increased by 20% and breadth is decreased by 40 % ,
we get the same perimeter. then the length and breadth of the new formed rectangular garden , respectively are
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        The solution by @josgarithmetic is not correct. The correct solution is placed below.
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Let L be the length and W be the width of the rectangular garden (the original dimensions). Then the first equation is 2L + 2W = 420, or L + W = 210. The second equation is 2*(1.2L) + 2*(0.6W) = 420, or 1.2L + 0.6W = 210. So, you have the system of 2 equations in 2 unknowns L + W = 210, (1) 1.2L + 0.6W = 210. (2) From eq(1) express W = 210-L and substitute it into eq(2). You will get 1.2L + 0.6*(210-L) = 210, 1.2L + 0.6*210 - 0.6L = 210 ====> 0.6L = 210 - 0.6*210 = 0.4*210 ====> L = = 140. Thus we just found L = 140 cm. Then W = 210 - L = 210 - 140 = 70 cm. The original length was 140 cm. The original width was 70 cm. Check. 140 + 70 + 140 + 70 = 420. ! Correct ! 2*140*1.2 + 2*70*0.6 = 420. ! Correct ! The new dimensions are: 1.2*L = 1.2*140 = 168 cm (length) and 0.6*W = 0.6*70 = 42 cm. Answer. The new dimensions are: 168 cm (length) and 42 cm (width).

Solved.

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