There are infinite possibilities....
To see why....look at the following graph.....where x = L and y = W and both are positive (i.e., in the first quadrant of the xy grid ).....
https://www.desmos.com/calculator/napzbq9xze
Notice that infinite first quadrant values on this curve have the characteristic that the product of their coordinates = 100 !!!!
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Given a line segment, a perpendicular bisector is a line (or segment) that intersects the given segment at right angles to the segment's midpoint.
Here's a pic....

AB is the given segment.....and CD is the perpendicular bisector
BTW.....Euclid presents this easy construction in his "Elements".... it is demonstrated here in a step-by-step fashion.....http://www.mathopenref.com/constbisectline.html
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