Question

A rectangular grassy lawn measuring 50m by 30m is to be surrounded externally by a path which is 3.5m wide. Find the cost of the levelling the path of the rate of RS 5 per square, m

Answer 1

Answer:

Rs.3045

Step-by-step explanation:

Length of lawn = 50 metres       (l)

 

Breadth of lawn = 30 metres      (b)

Width of path = 2 metres

Length of the lawn including the path = 50m + 3.5m + 3.5m

Length of the lawn including the path = 57 metres   (L)

Breadth of the lawn including the path = 30m + 3.5m + 3.5m

Breadth of the lawn including the path = 37 metres   (B)

Area of path = Area of lawn including path - Area of lawn

Area of path = (L×B) - (l×b)

Area of path = (57×37) - (50×30)

Area of path = 2109 - 1500

Area of path = 609 m^2

Cost of levelling  the path per m^2 = rs. 5

Cost of levelling the path = 609×5

Cost of levelling the path = rs. 3045

Cost of levelling the path is rs. 3045

Answer 2

Given :-

Length of lawn (l) = 50m

Breadth of lawn (b)= 30m

Width of path = 3.5m

To find :-

The cost of lavelling the path at Rs 5 per .sq.m

• Length of lawn including path

• 50+ 3.5×2

• 50+7= 57m

• Breadth of lawn including path

• 30+3.5×2

• 30+7 =37m

Length and breadth of lawn including path is 57 m and 37 m

$\bigstar{\boxed{\sf Area \ of \ rectangle = length \times breadth}}$

• Area of lawn

$\implies \sf Area \ of \ lawn = 50\times 30\\ \\ \implies\sf Area = 1500m^2$

$\therefore{\underline{\textsf {\textbf {Area \ of \ lawn = 1500m}}}}^2$

• First find the Area of lawn with path

$\implies\sf Area \ of \ lawn \ with \ path = 57\times 37\\ \\ \implies \sf Area = 2109$

$\therefore{\underline{\textsf {\textbf {Area \ of \ lawn \ with \ path = 2109m}}}}^2$

• Now the Area of path !

$\boxed{\sf{Area \ of \ path = Area \ of \ lawn \ including \ path - Area \ of \ lawn}}$

$\implies\sf Area \ of \ path = 2109-1500\\ \\ \implies\sf Area \ of \ path = 609m^2$

$\bigstar{\boxed{\textsf {\textbf {Area \ of \ path = 609m}}^2}}$

• Now the cost of levelling the path

• Rs 5 per sq.metre

$\implies \sf Cost= 609\times 5\\ \\ \implies\sf Cost\ of \ levelling =3045 \ Rs$

$\star{\boxed{\textsf {\textbf {Cost \ of \ levelling \ the \ path = 3045\ Rs}}}}$