Math
posted by Anonymous on .
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?

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
(w30)^2 = A/2 + 900
so
w = 30
then L = 120  60 = 60 
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. 
Thanks