Question

A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river.
if the farmer does not fence the side along the river, what is the largest area that can be enclosed?

Answer 1

Answer:

The largest Area = 2,000,000 m²

Step-by-step explanation:

Let the length = L and the width = W

A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river.

if the farmer does not fence the side along the river

So, the perimeter = L + 2W = 4000

So, L = 4000 - 2W ⇒(1)

Area = A = LW

Substitution with L from (1) at equation of area

∴A = (4000-2W)*W = 4000W - 2W²

At maximum area:

$\frac{dA}{dW}=4000-4W=0$

Solve for W

4000 - 4W = 0

4W = 4000

W = 4000/4 = 1000 meter

L = 4000 -2W = 4000 - 2* 1000 = 4000 - 2000 = 2000

So, the largest Area = LW = 2000 * 1000 = 2,000,000 m²