Using the same notation as Penny's answer to Kay,

8 = y + x + y = x + 2y, and
y = ^x/_Sqrt(2)

Substituting y from the first equation into the first and simplifying gives

x = ⁸/_{1 + Sqrt(2)}

which is 3.314 inches, or twice the length of the sides of Kay's window. Changing to more standard measurements this is 3 feet 3 and ³/₄ inches.

Now I am going to ask you what Penny asked Kay. When you have built the playhouse send us a photograph. We often get askwd "When will I ever use Pythagora's Theorem?" and this gives a nice reply.

Harley