2. a farmer has 400 meters of fence with which to enclose a portion of land. the farmer wants to enclose a rectangular piece of ground that is as large as possible. the land is bordered by water on two sides.
There are three options for the farmer
Option 1) have two sides bordered by the water and two sides by the fence
Option 2) have one side bordered by water and three sides by the fence
Option 3) use fence for all four sides
Construct formula for the area in each of the three options( hint: name one side x)
i don't know if my formulas are correct
What are your formulas?
To determine the formula for the area in each of the three options, we can start by representing the sides of the rectangular piece of land using variables.
Let's assume that one side of the rectangle is represented by "x" (in meters). Based on the given options, we can derive the following formulas for the area of the rectangle in each scenario:
Option 1:
In this case, two sides are bordered by water, and the remaining two sides are bordered by the fence. Let's label the other side as "y." Therefore, the area (A) can be calculated as:
A = x * y
Option 2:
Here, one side is bordered by water, and three sides are bordered by the fence. Again, let's label the other two sides as "y" and "z" (adjacent to the water and fence, respectively). The formula for the area is:
A = x * y * z
Option 3:
For this choice, the farmer uses the fence for all four sides, creating a completely enclosed rectangular piece of land. In this case, the area is straightforward, as both sides are equal to "x." Thus, the formula becomes:
A = x * x
These are the formulas for calculating the area in each of the three options. By substituting the appropriate values for "x" and, if applicable, "y" and "z," you can find the maximum area possible.