Posted by **Anonymous** on Sunday, February 1, 2009 at 8:54pm.

If Steve has 120 feet of fence to make a rectangular kennel and he will use his house on one side, how would the dimensions be found for a kennel with the greatest area be found?

- Math -
**Damon**, Sunday, February 1, 2009 at 9:06pm
L + 2 w = 120

A = L w

A = (120 -2w)w = 120 w - 2 w^2

that is parabola opening down, find the vertex (I assume you do not know calculus which would be easier)

-2 w^2 + 120 w = A

complete square

w^2 - 60 w = -A/2

w^2 - 60 w + 30^2 = -A/2 + 900

(w-30)^2 = -A/2 + 900

so

w = 30

then L = 120 - 60 = 60

- Math -
**bobpursley**, Sunday, February 1, 2009 at 9:06pm
Area= LW

Perimeter= 2L+ W

dArea/dL= W + dW/dl

the last term you get from taking the derivative of the perimeter equation

0 (perimeter is constant)=2 + dW/dl

so put that in the darea/dl, set to zero, and solve for W.

- Math -
**Anonymous**, Sunday, February 1, 2009 at 9:13pm
Thanks

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