Grade 11 Math
posted by Stacy .
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 = (543x)/2 = 271.5x
Area, A = x(271.5x)=27x1.5x²
To get maximum area, diff. w.r.t. x and equate to zero.
dA/dx = 273x=0
x=9m
longer side = 279*1.5=13.5m
The dog run is 9m by 13.5 m total
Total area= 121.5 m²