The two smaller squares together
Squares on a right-angled triangle's sides hold 9, 16 and 25 tiles. Nine and sixteen make twenty-five.
- A square of 9 tiles.
- Add a square of 16 tiles.
- Together they match a square of 25 tiles.
- 9 + 16 = 25.
Rule: this is for a right-angled triangle. The long side's square equals the other two squares added up. Let a, b be the short sides, c the long one. a × a + b × b = c × c — usually written a² + b² = c². Here a² means a × a.
Try sides 7, 24 and 25: 49 + 576 = 625. And 25 × 25 = 625. Try sides 9, 40 and 41: 81 + 1600 = 1681. And 41 × 41 = 1681. Both match exactly.
Three whole numbers with a² + b² = c² are a Baudhayana triple. For example, (3, 4, 5) is one: 9 + 16 = 25. (6, 8, 10) is one too: 36 + 64 = 100.
Watch out!
a² + b² = c² does not mean a + b = c. Check it: 3 + 4 is 7, not 5. The squaring is not extra. It is what makes the rule true.
Flip the switch. Do the small squares fill the big one?
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