Question

a rectangular lawn of length 50 m and breadth 25 m is to be surrounded externally by a path which is 2 m wide . find the cost of turfing the path at rate of ruppes 4per m2

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Cost of turfing the surrounded path = Rs. 1264

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

First find the area of rectangular lawn

Length of the rectangular lawn = 50 m

Breadth of the rectangular lawn = 25 m

$\boxed{\sf{Area\:of\:rectangle = Length \times Breadth}}$

Area of the rectangular lawn = $50 \times 25=1250$

So, Area of rectangular lawn = 1250 m²

Now find the area of rectangular lawn along with surrounded path

Width of the surrounded path = 2 m

Length of the rectangle lawn along with surrouded path = Length of the rectangular lawn + width of the surrounded path + width of the surrounded path = 50 + 2 + 2 = 54 m

Breadth of the rectangle lawn along with surrouded path = Breadth of the rectangular lawn + width of the surrounded path + width of the surrounded path = 25 + 2 + 2 = 29 m

$\boxed{\sf{Area\:of\:rectangle = Length \times Breadth}}$

Area of the rectangle lawn along with surrouded path = $54 \times 29 = 1566$

So, Area of the rectangle lawn along with surrouded path = 1566 m²

Now subtract Area of rectangular lawn from Area of the rectangle lawn along with surrouded path

Area of surrouded path = Area of the rectangle lawn along with surrouded path - Area of the rectangle lawn along with surrouded path = 1566 - 1250 = 316 m²

So, Area of surrounded path = 316 m²

Now we can find the cost of turfing the surrounded path

Cost of turfing 1 m² = Rs. 4

Cost of turfing the surrounded path $= 316 \times 4= Rs. 1264$

So, Cost of turfing the surrounded path = Rs. 1264