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A rectangular dog run is to be enclosed by a fence and then divided into two smaller rectangular areas by a fence parallel to one of the sides. If 54m of fence is available, find the dimensions of the dog run of greatest possible area. State the total area

Let x be the shorter side.
Longer side = (54-3x)/2 = 27-1.5x
Area, A = x(27-1.5x)=27x-1.5x²
To get maximum area, diff. w.r.t. x and equate to zero.
dA/dx = 27-3x=0
x=9m
longer side = 27-9*1.5=13.5m
The dog run is 9m by 13.5 m total
Total area= 121.5 m²

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