Posted by **Stacy** on Tuesday, April 26, 2011 at 10:44pm.

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

- Grade 11 Math -
**MathMate**, Tuesday, April 26, 2011 at 11:30pm
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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