Question

the dimensions of a rectangular plot are 35m by 20m. a path of uniform width 2m is built along the border and inside it. find the cost of paving the path with bricks at ruppes 25per sq metre and also the cost of covering the remaining part of the plot with grass at rupees 19 per sq metre. PLEASE HELP ME FAST AND I MARK U AS THE BRAINLIST

Answer 1

Cost of paving the path with bricks is Rupees 5100.

Cost of covering remaining area of plot with  grass is Rupees 9424.

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)

$l=W-(2\times w)$

$l=35-(2\times2)$

$\therefore l =35-4$

$\therefore l=31\ m$

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

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

$b=W-(2\times w)$

$b=20-(2\times 2)$

$\therefore b=20-4$

$\therefore b=16\ m$

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

Now,

Area of rectangle ABCD = $L\times W$

$=35\times 20$

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

Now,

Area of rectangle PQRS = $l\times b$

$=31\times 16$        -------------------(from equation 1 and 2)

$\therefore$ 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)

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

Remaining area = Area of rectangle PQRS

$\therefore$ 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 $\times$ cost per square meter of paving

Cost of paving = 204 $\times$ 25 = 5100

$\therefore$ Cost of paving the path with bricks is Rupees 5100.

Now,

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

Cost of covering remaining area with grass = 496 $\times$ 19

Cost of covering remaining area with grass = 9424

$\therefore$ Cost of covering remaining area with grass is Rupees 9424.

Answer 2

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)

l=W-(2\times w)l=W−(2×w)

l=35-(2\times2)l=35−(2×2)

\therefore l =35-4∴l=35−4

\therefore l=31\ m∴l=31 m

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

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

b=W-(2\times w)b=W−(2×w)

b=20-(2\times 2)b=20−(2×2)

\therefore b=20-4∴b=20−4

\therefore b=16\ m∴b=16 m

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

Now,

Area of rectangle ABCD = L\times WL×W

=35\times 20=35×20

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

Now,

Area of rectangle PQRS = l\times bl×b

=31\times 16=31×16 -------------------(from equation 1 and 2)

\therefore∴ 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)

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

Remaining area = Area of rectangle PQRS

\therefore∴ 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 \times× cost per square meter of paving

Cost of paving = 204 \times× 25 = 5100

\therefore∴ Cost of paving the path with bricks is Rupees 5100.

Now,

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

Cost of covering remaining area with grass = 496 \times× 19

Cost of covering remaining area with grass = 9424

\therefore∴ Cost of covering remaining area with grass is Rupees 9424.