*(d) All round outside of a rectangular plot
there is a path 3 m broad. The length of
the rectangular plot is 14 m and its breath
is 10 m. What will be the cost of fencing
the inside and the outside of the path at
the rate of 15 per metre?
Answers
Given :
- All round outside of a rectangular plot there is a path 3 m broad.
- The length of the rectangular plot is 14 m and its breath is 10 m.
To find :
- The cost of fencing the inside and the outside of the path at the rate of 15 per metre.
Step-by-step explanation :
Suppose ABCD is the rectangular plot. There is a 3 m broad path all around it.
The figure PQRS made by the plot and road together is also a rectangle.
Length of rectangle ABCD = 14 m.
Breadth of rectangle ABCD = 10 m
Area of rectangle ABCD = length x breadth.
Substituting the values in the above formula, we get,
= 14 x 10
= 140.
Therefore, Area of rectangle ABCD = 140 m².
There is a 3 m broad path on each side of the rectangle plot.
∴ The length of rectangle PQRS = 14 + 3 + 3 = 20 m.
And the breadth of rectangle PQRS = 10 + 3 + 3 = 16 m.
The area of rectangle PQRS = length x breadth
Substituting the values in the above formula, we get,
= 20 × 16
= 320.
Therefore, The area of rectangle PQRS = 320 m².
Area of the path = The area of rectangle PQRS - Area of rectangle ABCD
Substituting the values, we get,
= 320 - 140
= 180
Therefore, Area of the path = 180 m².
Now,
Cost of fencing of the path = the rate of per metre × area of the path.
Substituting the values, we get,
= 15 × 180
= 2700.
Therefore, Cost of fencing of the path = Rs. 2700.
Answer:
cost of fencing is 2700