The perimeter of a pasture on level ground is 80 yards Its s

The perimeter of a pasture (on level ground) is 80 yards. Its shape is unknown. What is the largest possible area this pasture could be? If the sides of the pasture must be straight, what is its-largest possible area?

Solution

Let us consider area is in rectangular shape,

let width = x

then length = y

perimeter of rectangle = 2(x+y)

and area of rectangle = x*y

and relation between area and perimeter of rectangle is

Area = 1.5 Perimeter

So from above relation we can say,

Area of rectangular shape = 1.5 * 80

Area of rectangular shape = 120 yards

So for case

a) Largest possible area of this pasture = 120yards

b) For case b the shape will be rectangular and hence its area will be 120 Yards