A farmer is constructing a rectangular fenced in a pen to contain rabbits. There is 120m of fencing. Determine the maximum area of the pen and the dimensions.

Question

A farmer is constructing a rectangular fenced in a pen to contain rabbits. There is 120m of fencing. Determine the maximum area of the pen and the dimensions. 

for mathe teacher in the 11th grade

Answer 1

This method uses calculus:

let x be the length and y be the width. This is the limiting equation

EQ1: 2x + 2y = 120

Now we want to find the maximum area:

EQ2: Area = x*y

rearrange EQ1 to be x = (60-y) and plug in x into EQ2

new EQ2: A = (60-y)*y = 60y - y²

Now we have the area with only one dimension on the other side. We can take the derivative with respect to y and setting equal to zero to find the local max.

dA/dy = 60 - 2y = 0

so y = 30, now we can use EQ1 to solve for x and we find x also equals 30

Answer 2

area = Length * width

perimeter = 2* (length + width) = 120 m

-------> length +width = 120/2 = 60

------> length + width =60

area would be 900 m^2 and dimensions would be 30 length and 30 width