The Landlord's Garden

The diagonal is exactly 20√13 ≈ 72.11 metres. Murugan needs to buy 73 paving stones — 72 for the full metres and 1 extra for the remaining 0.11 metres, since stones cannot be purchased in fractions.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. A rectangle's diagonal is the hypotenuse of a right triangle formed by the two sides. Step 1: The rectangle has length 60 m and width 40 m. Draw the diagonal — it forms a right triangle with legs of 60 m and 40 m. Step 2: Apply Pythagoras: D² = 60² + 40² = 3600 + 1600 = 5200. Step 3: D = √5200. Simplify: 5200 = 400 x 13. So √5200 = √400 x √13 = 20√13. Step 4: Calculate numerically: √13 ≈ 3.6056. So D ≈ 20 x 3.6056 = 72.11 metres. Step 5: Murugan needs 72.11 metres of paving stones. Since stones come in 1-metre units, he must buy 73 stones (you cannot buy 0.11 of a stone — the partial metre still needs a full stone). Step 6: The exact answer is 20√13 metres. The practical answer is 73 stones. Key Insight: The Pythagorean theorem is the foundation of all distance calculations in flat 2D space. The gap between the exact answer (20√13) and the practical answer (73 stones) illustrates a real-world consideration that pure mathematics ignores: physical materials come in discrete units, so always round up when buying materials.