Question

3.1 Q18

Find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer 1

The area is equal to length times width.
`A=lw`

The perimeter is equal to twice the sum of the length and the width.
`p=2l+2w`

We know that the perimeter is 450 meters, the length is
`450-2x` meters, and the width is
`x` meters.

To maximize the area, we find the global maximum of the function
`a(x)=x(450-2x)`. The easiest way is to use the formula for the vertex,
`x= (-b)/(2a) = 450/4 = 112.5 \ m`, and
`f( (-b)/(2a))=f(112.5)=25,312.5 \ m^2`.

I realize it sounds like a big number, but the largest area that can be enclosed is 25,312.5 m^2 (if I did this correctly!).