The perimeter of the rectangle is twice the sum of its length and its width. The dimensions of the fields can be represented as shown below.
What is the perimeter of the rectangle?
The perimeter of the rectangle is twice the sum of its length and its width.
[tex]\rm \text{Perimeter of rectangle}=2[(Length)+(Width)][/tex]
As it is given that the perimeter of the square carrot field is 96 ft, therefore, the side of the carrot field can be written as,
[tex]\rm \text{Perimeter of square} = 4\times (side)[/tex]
[tex]\rm 96 = 4\times (side)\\\\Side = 24\ ft[/tex]
Since the width of the completed field is 24 ft while the length of the complete field is 62 ft, therefore, the area of the field can be written as,
[tex]\text{(Area of lettuce)} + \text{(Area of Carrot)} + \text{(Area of Radishes \& Celery)} = (24 \times 62)\rm\ ft^2\\\\\text{(Area of lettuce)} + (24^2)\ ft^2 + (528)\ ft^2 = (24 \times 62) \ ft^2\\\\\text{(Area of lettuce)} + 576\ ft^2 + 528\ ft^2 = 1488\ ft^2\\\\\text{(Area of lettuce)} = 384\ ft^2\\\\L \times 24 = 384\ ft^2\\\\L = 16\ ft[/tex]
Let the width of the celery be x. And since the combined width of the radishes and the celery is 24 ft (Side of the square), therefore, the width of radishes is (24-x) ft.
Now the length of the portion with radishes and celery can be written as,
[tex]\rm \text{Length of Celery field} = 62-16-24 = 22\ ft[/tex]
Given that the perimeter of the Celery is 64 ft² and the length is 22 ft, therefore, the perimeter of the celery field can be written as,
[tex]\text{Perimeter of Celery field} = 2({\rm Length+ width})\\\\64 = 2(22 +x)\\\\64=44+2x\\\\64-44=2x\\\\20=2x\\\\x=10[/tex]
[tex]\text{Width of Radishes} = (24-x) = (24-10) = 14\rm\ ft^2[/tex]
Hence, the dimensions of the fields can be represented as shown below.
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