Answer:
The largest area will be 2812.5 square meters.
Step-by-step explanation:
The perimeter of rectangle is given as:
(L is the length and W is the width)
As one side is not to be fenced, so the formula here will be : 
Perimeter is 150.
So,
; 
Area of the rectangle is : 
Plugging the value of L in the area formula;
Area = 
This is a parabola or quadratic function whose maximum or minimum values occur at the average of the solutions.
So, Solving 
=>
Or 
=> 
=> 
W = 75
So, the two solutions are zero and 75.
The average of them is 
Now, the maximum area is at W=37.5
And 
L = 75
The dimensions that maximize the area are L=75 and width W=37.5
And maximum area =
= 2812.5 square meters
Hence, the largest area will be 2812.5 square meters.