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Length times width equals area
All that can definitely be said is that length plus width = 50 feet.
To find the relationship in width and area you can use the formula area/length = width. To find the area of a room you multiple the length by the width.
the perimeter is all of the sides added up, the length and width would only give you half of the perimeter i think...
The answer will depend upon what shape the object is. For example, if the shape was a rectangle then the perimeter = (length + width) * 2. If the shape was something different then the relationship would also be different.