Question

(6)
5. The dimensions of a rectangular plot are 35 m by 20 m. A path of uniform width 2 m is
built along the border and inside it
. Find the cost of paving the path with bricks at 7 25 per
square metre and also the cost of covering the remaining part of the plot with grass at
19 per square metre.​

Answer 1

Answer:

Step-by-step explanation:

Refer attached figure.

Given:- In Rectangular plot ABCD,

Length(L) AD=BC = 35 m, Width (W) AB=DC=20 m.

path width(w) = 2 m .

Cost per square per meter of paving with bricks = Rupees 25.

Cost per square metre for covering remaining area with grass = Rupees 19.

To find:- cost of paving the path with bricks=?

cost of covering remaining part of the plot with grass=?

Solution:-

Refer attached figure.

Let the rectangular plot be ABCD, and the inscribed rectangle be PQRS.

Now,

Length of rectangle PQRS (l) = length of rectangle ABCD(L) - 2 times the width of path(w)

Therefore length of rectangle PQRS () = 31 m.  ---------(equation 1)

Width of rectangle PQRS (b) = Width of rectangle ABCD(W) - 2 times the width of path(w)

Therefore width of rectangle PQRS () = 16 m.   ----------(equation 2)

Now,

Area of rectangle ABCD =

Area of rectangle ABCD = 700 square metre.    --------(equation 3)

Now,

Area of rectangle PQRS =

       -------------------(from equation 1 and 2)

Area of rectangle PQRS = 496 square metre.    ---------(equation 4)

Now,

Area of path = Area of rectangle ABCD - Area of rectangle PQRS

Area of path = 700-496               -----------(from equation 3 and 4)

Area of path = 204 square metre.     -------------(equation 5)

Remaining area = Area of rectangle PQRS

Remaining Area = 496 square meter.      ----------------(equation 6)

Now,

Cost of paving the path with brick at rupees 25 per square metre.

Cost of paving=total area of path  cost per square meter of paving

Cost of paving = 204  25 = 5100

Cost of paving the path with bricks is Rupees 5100.

Now,

Cost of covering remaining area with grass = remaining area  cost per square metre  for covering with grass

Cost of covering remaining area with grass = 496  19

Cost of covering remaining area with grass = 9424

Cost of covering remaining area with grass is Rupees 9424.