Question

The length and breadth of a park are in the ratio 2:1 and its perimeter is 240m.A path 2m wide runs inside it,along its boundary.Find the cost of paving the path at 3 per sq m.

Answer 1

Let the length be 2x and breadth x
By the problem,
2(2x+x) = 240
2(3x)= 240
3x = 240/2
3x = 120
x = 120/3
x = 40

Length = 80m
Breadth = 40m
Area = (80*40)m
$= 3200m^{2}$
Length of the park inside the path = (80-2)m = 78m
Breadth of the park inside the path = (40-2)m = 38m
Area of the park inside the path = (78*38)m
$= 2964m ^{2}$
Area of the path = outer area - inner area
$=( 3200 - 2964)m ^{2}$
$= 236m ^{2}$
Cost of paving the path @ Rs 3/sq m
= Rs 3*236
= Rs 708

Answer : The cost of paving the path would be Rs 708.

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