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.

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=(2040)/(2)=1020\\\\x+2x=1020\\\\3x=1020\\\\x=(1020)/(3)\\\\x=340`

So, the length would be
`2x=2* 340=680\ feet`

If another field is square,

So, the dimensions would be

`4* side=2040\\\\side=(2040)/(4)=510\ feet`

Now, Area of rectangle would be

`Length* breadth=340* 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.