a farmer has 600 meters of fencing and plans to use it to build two adjacent rectangular pens as show above. the farmer would like the total area of the two pens to be 1000 square meters. write an equation to determine the value of x? My solution is: 3X^2 - 600X + 2000= 0

is this correct?

That's what I get, too.

To find the equation to determine the value of x, let's break down the problem step by step.

First, let's define the variables:
Let's assume the longer side of the rectangular pen is x meters.
The width of each pen is given as half of the length since they are adjacent. So, the width of each pen is (x/2) meters.

Now, let's calculate the perimeter of the two pens. For each pen, we have two lengths and two widths, so the total perimeter is:

Perimeter of one pen = 2x + 2(x/2) = 3x

Since we have two pens, the total perimeter will be:

Total perimeter = 2 * (3x) = 6x

According to the problem, the farmer has 600 meters of fencing available, so we can set up the equation:

6x = 600

Now, let's find the value of x:

6x = 600
Divide both sides by 6:
x = 100

So, the value of x is 100.