Question

a farmer plans to fence a rectangular field adjacent to a river. the field must contain 125000 square meters in order to have enough space for his crops. no fencing is needed along the river. what is the minimum amount of fencing that will be needed?

Answer 1

On solving the provided question we got to say that - 500 meters long, and 250 meter wide

What is derivative?

Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). Problems involving calculus and differential equations need the use of derivatives.

125000 square meters  of area = l X w is =  length times width

$l=125000/w$

Fencing =$Perimeter = P = L+2W= 125000/W +2W$

Now,

derivative set = 0

P'(X) =  2 -125000/W^2 = 0

           $2W^2 = 125000\\ W^2 = 62500\\ W = 250meters wide$

          $L =125000/250= 500 meters long, the side parallel to the river$

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