The ratio of length and width of a park is 3 : 1. The perimeter of the park
is 320 meters. A 2m wide path has been made along the inner edges of the
park. What will be the total cost of constructing the road at the rate of 1.5
per square metre?
Answers
Step-by-step explanation:
Given:-
The ratio of length and width of a park is 3 : 1. The perimeter of the park is 320 meters. A 2m wide path has been made along the inner edges of the
park.
To find:-
What will be the total cost of constructing the road at the rate of 1.5 per square metre?
Solution:-
The ratio of length and width of a park is 3 : 1.
Let the length of the park be 3X m
Let the width of the park be X m
We know that
Perimeter of a rectangle = 2(l+b) units
We have. l = 3X m and b = X m
On Substituting these values in the above formula
=> P = 2(3X+X) m
=> P=2(4X) m
=> P = 8X m
According to the given problem
The perimeter of the park is 320 m
=> 8X = 320
=> X = 320/8
=> X = 40 m
Now , 3X = 3×40 = 120 m
Length of the park = 120 m
Width of the park= 40 m
Area of a rectangle = lb sq.units
Area of the park = 120×40=4800 sq.m
If 2 m width path has been made along its edges inner side then
Length of the Park will be
120-(2×2)
=120-4
=116 m
Breadth of the park will be
40-(2×2)
=40-4
=36 m
Area of a rectangle = lb sq.units
Area of the given park
= 116×36 sq.m
=4176 sq.m
Area of the remaining park = 4176 sq.m
Area of the Path =
Total area of the park - Area of the remaining park
=> 4800-4176
=> 624 sq.m
Area of the path = 624 sq. m
The cost of the constructing the road in the path of 1 sq.m = Rs. 1.5
Total cost of constructing the road in the total path of 624 sq.m
=> 624×1.5
=> Total cost Rs. 936
Answer:-
Total cost of constructing the road in the total path is Rs. 936
Used formulae:-
- Perimeter of a rectangle = 2(l+b) units
- Area of a rectangle = lb sq.units
- l=length
- b=breadth
- w=width