Given 50 ft. of wall in a L-shaped room, how to find x and y, to produce the largest area?

Question

Given 50 ft. of wall in a L-shaped room, how to find x and y, to produce the largest area?

Answer 1

Largest area will be when x = y.

Thus, using just 50 linear feet of wall:

  A 25 x 25 room has 625 sq. feet of floorspace.

  A 49 x 1 room (unlikely) has 49 sq. feet of floorspace.

The closer to "square" you get, the more floor space becomes available.

Hope that helped.