Question

Juan wishes to build a garden at the bottom of his property. He wants to split it in two, like the diagram below, so he can plant vegetables in one side and fruit in the other. There is a stream at the bottom of his property so he doesn't have to fence there. He has 120 feet of fencing.

Answer 1

Answer:

20 ft by 60 ft

Step-by-step explanation:

"What should the dimensions of the garden be to maximize this area?"

If y is the length of the garden, parallel to the stream, and x is the width of the garden, then the amount of fencing is:

120 = 3x + y

And the area is:

A = xy

Use substitution:

A = x (120 − 3x)

A = -3x² + 120x

This is a downward facing parabola.  The maximum is at the vertex, which we can find using x = -b/(2a).

x = -120 / (2 · -3)

x = 20

When x = 20, y = 60.  So the garden should be 20 ft by 60 ft.