The Baudhayana–Pythagoras Theorem

In a right-angled triangle the square on the longest side equals the sum of the squares on the other two. The converse tests for a right angle.

Key ideas

• The hypotenuse is opposite the right angle and is the longest side.
• Baudhayana stated the result in the Sulba Sutras, long before Pythagoras.
• If the sides satisfy a² + b² = c² (c longest), the triangle has a right angle opposite c.
• Pythagorean triples are whole-number solutions: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25. Multiples of a triple are triples too.
• For a ladder against a wall, the ladder is the hypotenuse and the wall and ground are the other sides.

Remember

Watch out

• Adding the squares when the hypotenuse is given and a shorter side is missing (subtract instead).
• Checking a² + b² = c² with c not the longest side.
• Forgetting to take the square root at the end.

Worked example