Question

A farmer has 2400 m of fencing and wants to enclose a rectangular field bordering a river, with no fencing needed along the river. Let x represent the width of the field. Complete parts (a) through (d).

Answer 1

To solve this problem, we can set up an equation to represent the perimeter of the rectangular field. The width of the field is 600 m.

Step-by-step explanation:

To solve this problem, we can set up an equation to represent the perimeter of the rectangular field. Let's let x represent the width of the field. Since the width is perpendicular to the river, we can assume that the length of the field is along the river. The perimeter is then 2x + L, where L is the length of the field.

We are given that the total length of fencing available is 2400 m, so we can set up the equation 2x + L = 2400. We can rearrange this equation to solve for L: L = 2400 - 2x.

Now we can substitute this expression for L into the perimeter equation: 2x + (2400 - 2x) = 2400. Simplifying this equation gives us 4x = 2400, and dividing both sides by 4 gives us x = 600.

Therefore, the width of the field is 600 m.