area = A = L * B where L is length and B is width
Say back wall is one length
then
30 = L + 2B
or
L = 30 - 2 B
then
A = (30-2B)* B
A = -2B^2 + 30 B
That is a downward opening parabola (sheds water)
We want the axis of symmetry which contains the vertex which is at the top (maximum A)
So complete the square
B^2 -15 B = - A/2
B^2 - 15 B + 225/4 = -A/2 + 225/4
(B-15/2)(B-15/2) = -A/2 + 225/2
B = 15/2 = 7.5 feet
L = 30 - 2(7.5) = 15 feet
Charles wants to build a vegetable garden such that three sides of the garden are fenced and the fourth side of the garden will be the existing back fence. He has 30 feet of fencing available. Find the dimensions of the garden that will produce the maximum enclosed area
1 answer
1 answer