What is the area of the largest rectangular field that can be completely enclosed
using 120 feet of fencing?
In order to find the area of the largest rectangular field that can be completely enclosed using 120 feet of fencing, we need to maximize the area of the rectangle.
A rectangle has two sides of equal length and two sides of equal width. Let's say the width of the rectangle is x feet. Therefore, the length of the rectangle would also be x feet.
The perimeter of a rectangle is the sum of all four sides, which in this case is 2 times the length plus 2 times the width:
Perimeter = 2x + 2x = 4x
We are given that the perimeter is equal to 120 feet, so we can set up the equation:
4x = 120
To solve for x, we divide both sides of the equation by 4:
x = 120/4
x = 30
So, the width and length of the rectangle are both 30 feet.
To find the area of the rectangle, we use the formula:
Area = length × width
Area = 30 × 30
Area = 900 square feet
Therefore, the largest rectangular field that can be completely enclosed using 120 feet of fencing has an area of 900 square feet.