A rectangular garden is made at the side of the house. Part of the house forms one side of the fencing and divided into four equal plots. If 90m of fencing is available, determine the dimensions for the entire garden that will produce a maximum area.
how can i come up with a quadratic equation from this problem????
Sketch the problem
You need 5 lengths of fence of length w and 1 length e for end
area = A = w e
5 w + e = 90
5 w + A/w = 90
5 w^2 - 90 w + A = 0
where did you get 5?
Now if you do not know calculus, find the vertex of the parabola by completing the square
5 w^2 - 90 w = -A
w^2 - 18 w = -A/5
w^2 -18 w + 81 = -A/5 + 81
(w-9)^2 = -(1/5)(A - 405)
so max at w = 9 , A = 405
then
5 (9) + e = 90
45 + e = 90
e = 45
so 45 by 9
i know how to get the vertex and all the other stuff,
i just don't understand where did you get 5?
To get 5, DRAW A Picture
9 foot fence at 0, 11.25 , 22.5 , 33.75 , 45
and a 45 foot fence across the end
four fence sections requires five posts :)
because you need one at the start, zero.
(unless you close the figure topologically by joining the last section to the first.)
aah ok.. thanks a lot!!!;)
0, 11.25 , 22.5 , 33.75 , 45
notice four commas seperating five numbers