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
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
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
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