The two smaller squares together
Show on a big screenSquares 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?
Loading lab…
Try the lab to finish this lesson.