Asked by gilly
A rectangular garden next to a building is to be fenced with 120 feet of fencing. The side against the building will not be fenced. What should the lengths of the other three sides be in order to assure the largest possible area?
Answers
Answered by
Damon
2 w + L = 120 so L = (120-2w)
A = w L = w (120-2w) = 120 w - 2w^2
y = A/2 = 60 w - w^2
maximize A/2 same as max A
w^2 - 60 w = -y
w^2 - 60 w + 900 = -y + 900
(w-30)^2 = -(A/2) + 900
vertex at w = 30
the L = 120-60 = 60
so
30, 30 and 60
A = w L = w (120-2w) = 120 w - 2w^2
y = A/2 = 60 w - w^2
maximize A/2 same as max A
w^2 - 60 w = -y
w^2 - 60 w + 900 = -y + 900
(w-30)^2 = -(A/2) + 900
vertex at w = 30
the L = 120-60 = 60
so
30, 30 and 60
Answered by
gilly
wow you rock thanks a bunch x
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.