Question

length and breadth of the park are in the ratio 3:2 the perimeter of this park is 240m. there is a 3m wide walk way around the inside of the park.with these input the size of the walk way can be calculated.the cost for cementing is given as RS.120per SQ.m. with this information,total cost for cementing the walk way can be calculated as Rs.82080. we coding for this question.​

Answer 1

Let us assume the length of the park be 2x

Let us assume the breadth of the park be x

From the question is given that,

Perimeter of the park = 240 m

Wide of the path = 2 m

Rate of paving the path = ₹ 80 per m2

Then,

Perimeter of the park = 2 (l + b) = 240

= 2 (2x + 1x) = 240

= 2 (3x) = 240

= 6x = 240

= x = 240 /6

= x = 40

Then,

The length of the park be 2x = 2 × 40 = 80 m

The breadth of the park be x = 40 m

Let PQRS be the given park and

ABCD be the inside boundary of the path.

Area of the park PQRS = (l × b)

= (80 × 40) = 3200 m

2 Wide of the path = 2 m

Then,

AB = (80 – (2 × 2)) = (80 – 4)

= 76 m AD

= (40 – (2 × 2)) = (40 – 4) = 36 m

∴Area of the rectangle ABCD = (76 × 36) m2 = 2736 m2

Area of the path = (Area of PQRS – Area of ABCD)

= (3200 – 2736) = 464m2

Rate of paving the path = ₹ 80 per m2

∴Total cost of paving the path of a park = ₹ (80 × 464) = ₹ 37120