Question

A square flower bed is kept in the centre of a square field of side 52m leaving a path all around the flower bed. the cost of putting the square bed and gravelling the path is rs 2.75 and rs 1.50 per m2 is 6936. find the width of the path

Answer 1

Let width of the gravel path be x metres.

∴ each side of the square flower bed = (44 – 2x) metres



Now, area of square field = 44 × 44 = 1936 m2

Area of flower bed = (44 – 2x) × (44 – 2x)

= (44 – 2x)2 m2 

∴ Area of gravel path = Area of field – Area of flower bed

= 1936 – (44 – 2x)2

= 1936 – (1936 – 176x + 4x2)

= 1936 – 1936 + 176x –4x2

= (176x – 4x2) m2

Cost of laying the flower bed = (Area of flower bed) × (Rate per sq.m.)



Cost of gravelling the path = (Area of gravel path) × ( Rate per sq.m.)



Given, total cost of laying the flower bed and gravelling the path is Rs 4904

∴ 11(22 – x)2 +6 (44x – x2) = 4904

11(484 + x2 – 44x) + (264x – 6x2) = 4904

5324 + 11x2 – 484x + 264x – 6x2 = 4904

5x2 – 220x + 420 = 0

x2 – 44x + 84 = 0

x2 – 42x  – 2x + 84 = 0

x(x – 42) – 2(x – 42) = 0

(x – 2)  (x – 42) = 0

x = 2  or  x = 42

x ≠ 42, ∵ side of square is 44 m

Therefore x = 2 m

Hence, the width of gravel path is 2 metres.