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.

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,

So, the length would be

If another field is square,

So, the dimensions would be

Now, Area of rectangle would be

Area of square would be

sq. ft

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

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