SOLUTION: A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens (see figure). The gardener wants the enclosed area to be 336 square meters. What dimensions should

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Question 1067790: A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens (see figure). The gardener wants the enclosed area to be 336 square meters. What dimensions should the gardener use to obtain this area? (Round your answers to two decimal places.)
4x+3y=100
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
The gardener/the fence has 3 times the length L and 2 times the width W (it is the FULL wide, not its half).

So the equations are

3L + 2W = 100,       (1)
L*W = 336.           (2)


From (1), W = . Substitute it into (2) replacing W. You will get

 = 336,   or

L*(100-3L) = 672,

100L - 3L^2 = 672,

3L^2 - 100L + 672 = 0.


 =  = .


 =  = 24         --->   =  = 14.


 =  =          --->   =  = 36.


Answer.  There are two solutions: 1) the rectangle has the outer dimensions 24 m and 14 m;

                                  2) the rectangle has the outer dimensions  m and 36 m.


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