Question

A farmer has 2040 feet of fencing and wishes to fence off two separate fields. One of the fields is to be a rectangle with the length twice as long as the width, while the other field is to be a square. Determine the dimensions of the fields if the framer wishes to maximize the total area of the two fields.

Answer 1

Answer: Dimensions should be 510 feet to maximize the total area of the two fields.

Step-by-step explanation:

Since we have given that

Perimeter of field = 2040 feet

Let the width of rectangle be 'x'

Let the length of rectangle be '2x'

So, According to question, it becomes,

$2(l+b)=2040\\\\l+b=\dfrac{2040}{2}=1020\\\\x+2x=1020\\\\3x=1020\\\\x=\dfrac{1020}{3}\\\\x=340$

So, the length would be $2x=2\times 340=680\ feet$

If another field is square,

So, the dimensions would be

$4\times side=2040\\\\side=\dfrac{2040}{4}=510\ feet$

Now, Area of rectangle would be

$Length\times breadth=340\times 680=231200\ ft^2$

Area of square would be

$Side^2=510^2=260100$ sq. ft

So, Dimensions should be 510 feet to maximize the total area of the two fields.