CBSE Class 8 Annual Assessment

Chapter 2: The Baudhayana-Pythagoras Theorem

Summary

Rooted in Baudhayana’s Sulba-Sutra (c. 800 BCE), this chapter builds to the theorem on right triangles. It starts by doubling a square: the square on a diagonal has twice the area of the original, so an isosceles right triangle with legs \(1\) has hypotenuse \(\sqrt{2}\), and in general \(c^2 = 2a^2\). The number \(\sqrt{2} \approx 1.41421356\ldots\) is shown to be neither a terminating decimal nor a fraction \(\dfrac{m}{n}\) — an early proof of irrationality. Combining two different squares leads to the central result: for a right triangle with legs \(a, b\) and hypotenuse \(c\), \(a^2 + b^2 = c^2\). Baudhayana was the first to state this in general form, centuries before Pythagoras. Integer solutions like \((3, 4, 5)\) and \((5, 12, 13)\) are called Baudhayana (Pythagorean) triples; scaling any triple by \(k\) gives another, so infinitely many exist, and primitive triples have no common factor. The chapter touches Fermat’s Last Theorem and applies the theorem to diagonals, rhombuses and a classic lake-and-lotus problem.

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