a path 1m wide is built inside a square park of side 30m along its sides. find the area of the path. calculate the cost of constructing the path at the rate of 70 per m2.
Answers
side of square park (A) = 30m
width of path = 1m
side of inner park (a) = 30-1-1 = 28m
cost of construction = 70 per m^2
Area of path = Area of square park - area of park inside the path
= A^2 - a^2
= 30^2 - 28^2
= 900 - 784
= 116m^2
Cost of construction of path = 70×116
=8120
Given:
A square park of side 30m around which a path of width 1m is built.
To find:
The area of the path and the cost of constructing the path at the rate of 70 per m².
Solution:
With reference to the diagram, the path around the park is of yellow color with a width of 1m.
We know that area of a square is:
Area = (side)²
Area of the outer square park with side 30m = (30)²= 900m².
Side of the inner square park = 30 - 1 - 1 = 28m.
Area of the inner square park with side 28m = (28)² = 784m².
Area of the path = Area of the outer square park - Area of the inner square park = 900 - 784 = 116m².
Now, we know that for 1m², the cost of constructing the path is 70 Rs.
So, The cost of constructing 116m² = 116×70 = 8120 Rs.
Therefore, the area of the path is 116m² and the cost of constructing the path at the rate of 70 per m² is 8120 Rs.
