The dimensions of the rectangle are:
l = 50 m
b = 
m
<h3>What is a perimeter in math?</h3>
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides.
<h3>How do we find a perimeter of a rectangle?</h3>
The perimeter of a rectangle,denoted by P is given by the formula, P=2l+2b, where l is the length and b is the breadth of the rectangle.
<h3>
Given:</h3>
As per the question:
Perimeter of the room is given as P = 200 m
The region is rectangular having a semicircle at each end.
Now,
Let 'l' be the length of the rectangle, 'b' be its breadth and 'r' be the radius of the semi-circle at each end.
Then, Area of the given rectangle, A = lb
Perimeter of the room, P is =
Therefore, 
Now,
Area, A = 
Now, differentiate A w.r.t l:
Again differentiating w.r.t 'l', we get:
< 0
Thus we get maximum are when 
Therefore,
l = 50 m
Now, from
To know more about area of a recatangle, visit the link
brainly.com/question/20693059
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