Homework Help: Grade 11 Math

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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