Question

There is a square field whose side is 10 m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and gravelling the path at ₹ 3 and ₹ 4 per square metre respectively is ₹ 364. Find the width of the gravel path.

Answer 1

Area of the flower bed = a²

Area of the gravel path = 100 – a²

Area of total garden = 100

Given cost of flower bed + gravelling = Rs 364

3a² + 4(100 – a²) = Rs 364

3a² + 400 – 4a² = 364

∴ a² = 400 – 364

= 36 ⇒ a = 6

Width of gravel path = `(10 – 6)/2` = `4/2` = 2 cm