The Baudhayana-Pythagoras Theorem

Overview

This chapter presents the famous theorem on right-angled triangles, known in ancient India through Baudhayana and elsewhere as the Pythagoras theorem. It relates the lengths of the three sides and has wide use in geometry and measurement.

Key concepts

• In a right-angled triangle the side opposite the right angle is the hypotenuse, the longest side.
• The square on the hypotenuse equals the sum of squares on the other two sides.
• A Pythagorean triple is three whole numbers satisfying the theorem, e.g. 3, 4, 5.
• The converse lets us test whether a triangle is right-angled.

Important formulae

• c² = a² + b², where c is the hypotenuse.
• Hypotenuse c = √(a² + b²).
• Common triples: (3, 4, 5), (5, 12, 13), (8, 15, 17).

Solved example

1. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
2. c² = 6² + 8² = 36 + 64 = 100.
3. c = √100 = 10 cm.

Important questions

1. A ladder 13 m long rests against a wall with its foot 5 m away. How high does it reach?
2. Verify whether 9, 40, 41 form a Pythagorean triple.
3. The diagonal of a rectangle is 17 cm and one side is 8 cm. Find the other side.
4. Is a triangle with sides 7, 8, 12 right-angled? Justify.

Quick revision

For right triangles, square of hypotenuse = sum of squares of the legs. Memorise common triples to save time, and use the converse to check for a right angle. Always identify the hypotenuse as the longest side.