Henry Ernest Dudeney/Puzzles and Curious Problems/204 - The Donjon Keep Window/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $204$

In The Canterbury Puzzles Sir Hugh de Fortibus calls his chief builder, and, pointing to a window, says:

"Methinks yon window is square, and measures, on the inside, one foot every way,

and is divided by the narrow bars into four lights, measuring half a foot on every side."

See our Figure $A$.

"I desire that another window be made higher up,

whose four sides shall also be each one foot,

but it shall be divided by bars into eight lights, whose sides shall be all equal."

This the craftsman was unable to do, so Sir Hugh showed him our Figure $B$, which is quite correct.

But he added, "I did not tell thee that the window must be square, as it is most certain it never could be."

Now, an ingenious correspondent, Mr. George Plant, found a flaw in Sir Hugh's conditions.

Something that was understood is not actually stated,

and the window may, as the conditions stand, be perfectly square.

How is it to be done?

Every side of every light of this window is of the same length.

It was never said that the lights should all be the same area.

The irregular lights are in fact $25\%$ larger than the square ones.