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What dimensions should the gardener use to obtain this area? (Round your answers

Mathematics
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A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens (see figure). The gardener wants the enclosed area to be 286 square meters.
x = m     and    y = m (smaller x-value)
x = m       and       y = m (larger x-value)

4x+3y=100

Mar 8th, 2015

Two rectangle areas =286

The fence will have width 3 times and length 4 times .

Each rectangle area= xy

2xy =286

xy =143

4x+3y =100

4xy = 572

(100-3y)y =572

3y2-100y+572=0

3y2 -78y-22y+572=0

3y(y-26)-22(y-26)=0

(y-26)(3y-22)=0

Y =26 or y =22/3

If y =26  then 4x = 100-78 =22  ;  x =5.5

If y =22/3  then  4x =100-22=78  ; x=19.5

Both the solutions are possible

If you want length larger then x =19.5 y =22/3

x= 19.5  ,  y =22/3 m

or

x=5.5 m,  y=26 m


Mar 8th, 2015

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