A rectangular courtyard has its length and width in the ratio 4:3. If the total cost to pave the courtyard is Rs. 600 at a rate of 50 paise per square meter, what is the length of the courtyard's diagonal?

Explanation

First, calculate the total area paved: Rs. 600 at 50 paise (Rs. 0.50) per m² means the area is 600 / 0.5 = 1200 m². Let the sides be 4x and 3x, so area = 12x² = 1200, giving x² = 100 and x = 10. Therefore, the sides are 40 m and 30 m. The diagonal is √(40² + 30²) = √(1600 + 900) = √2500 = 50 m.