To find: The dimensions of the field of largest area that a farmer can fence.
The dimensions of the field of largest area that the farmer can fence is by .
A farmer has of fencing and wants to fence off a rectangular field that borders a straight river. The farmer doesn’t fence along the river.
As per given, assume that the length of the rectangular field is equal to .
As the length is fenced two times i.e. length of the fence for these two sides is equal to and as the total fence is . So, the breadth of the rectangular field is equal to .
Use the formula for the area of the rectangular region.
So, the area function of the rectangular region is given by . To maximize the area of the rectangular region graph the area function .
To graph a function , follow the steps using graphing calculator.
First press “ON” button on graphical calculator, press key and enter right hand side of the equation after the symbol . Enter the keystrokes .
The display will show the equation,
Now, press the key and key to produce the graph of given function in standard window as shown in Figure (1).
As observed from the graph, the area function has maximum value at .
So, the length of the rectangular region is equal to and the breadth of the rectangular region is equal to .
Therefore, the dimensions of the field of largest area that the farmer can fence is by .
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