Question

Math-- Farmer Bill has 500 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Bill does not fence the side along the river, find the length and width of the plot that will maximize the area. What is largest area that can be enclosed?

Answer 1

Required dimensions of the rectangle are L = 200 m, W = 100 m

The largest area that can be enclosed is 20,000 sq m.

Explanation:

The available length of the fencing = 500 m

Now, Perimeter of a rectangle = SUM OF ALL SIDES = 2(L+B)

But, here once side of the rectangle is NOT FENCED.

So, the required perimeter

= Perimeter of Complete field - Boundary of 1 open side

= 2(L+ W) - L = 2W + L

Now, fencing is given as 500 m

⇒ 2W + L = 500

Now, to maximize the length and width:

put L = 200, W = 100

we get 2(W) +L = 2(200) + 100 = 500 m

Hence, required dimensions of the rectangle are L = 200 m, W = 100 m

The maximized area = Length x Width

= 200 m x 100 m = 20, 000 sq m

Hence, the largest area that can be enclosed is 20,000 sq m.