Question

Farmer ed has 5000 meters of fencing and wants to enclose a rectanglular plot that borders on a river. if farmer ed does not fence the side along the river what is the largest area that can be enclosed. 5500-2x?

Answer 1

To find the largest area that can be enclosed with 5000 meters of fencing, we need to determine the dimensions of the rectangular plot. The largest area that can be enclosed is 3,125,000 square meters.

Step-by-step explanation:

To find the largest area that can be enclosed with 5000 meters of fencing, we need to determine the dimensions of the rectangular plot. Let's assume the length of the plot is x meters and the width is y meters. Since there are three sides of the plot that need to be fenced, the perimeter can be expressed as:

Perimeter = x + y + x = 2x + y

Given that the perimeter is 5000 meters, we have:

2x + y = 5000

To determine the largest area, we can express the area (A) as:

A = x * y

Since we want to maximize the area, we want to express the area in terms of a single variable. We can do this by solving the perimeter equation for y:

y = 5000 - 2x

Substituting this into the area equation:

A = x * (5000 - 2x)

Now, we can maximize the area by finding the vertex of the quadratic equation A = x(5000 - 2x).

The x-coordinate of the vertex can be found using the formula:

x = -b/2a, where a = -2 and b = 5000

Substituting in the values:

x = -5000/(2*-2) = 1250

Now, substituting this value of x back into the area equation:

A = 1250 * (5000 - 2*1250) = 1250 * 2500 = 3,125,000 square meters

Therefore, the largest area that can be enclosed is 3,125,000 square meters.