The Banner of St. George

The flag measures 4 feet by 3 feet, so its diagonal is 5 feet. “All you need to do is to deduct half the length of this diagonal (2 1/2 feet) from a quarter of the distance all round the edge of the flag (3 1/2 feet) — a quarter of 14 feet. The difference (1 ft.) is the required width of the arm of the red cross.”

Proof:

If the flag measures 4 feet by 3 feet, the red area is given by

4x + 3x – x² = 6,

so

x² – 7x + 6 = 0.

Solving the quadratic equation gives x – 3.5 = ± 2.5, and as x can’t be 6, the answer must be 1 foot.

From Dudeney’s Amusements in Mathematics, via Erwin Brecher’s Ultimate Book of Puzzles, Mathematical Diversions, and Brainteasers (1996).