# Thread: Function of an area problem

1. ## Function of an area problem

Given 1200 meters of fencing, a farmer needs to enclose three sides of a field (with the other side being a river).

Write a function finding the area (A) in terms of the width (x). The river is parallel with the length (y). Then using the function find the maximum area of the field.

Here's what I've done so far:

$\displaystyle A(x)=x(1200-2x)$ <- y=1200-2x, multiplied by the other X

Then I figured for the maximum area, it would be $\displaystyle \frac{-b}{2a}$ so $\displaystyle -2x^2+1200x$ and $\displaystyle \frac{-1200}{-4}=300$

Therefore the width of the maximum would be 300meters, with maximum area being 180,000 square meters.

2. Originally Posted by uberkrissy
Given 1200 meters of fencing, a farmer needs to enclose three sides of a field (with the other side being a river).

Write a function finding the area (A) in terms of the width (x). The river is parallel with the length (y). Then using the function find the maximum area of the field.

Here's what I've done so far:

$\displaystyle A(x)=x(1200-2x)$ <- y=1200-2x, multiplied by the other X

Then I figured for the maximum area, it would be $\displaystyle \frac{-b}{2a}$ so $\displaystyle -2x^2+1200x$ and $\displaystyle \frac{-1200}{-4}=300$

Therefore the width of the maximum would be 300meters, with maximum area being 180,000 square meters.
looks fine to me.