Question

A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs 7.50 per m?.​

Answer 1

Answer:

Given:

Length of the plot = 125 m

Breadth of the plot = 78 m

Area of plot ABCD = Length × Breadth

                               = 125×78

                               = 9750 $m^{2}$

Length of the plot including the path = ( 125 + 3 + 3)m = 131m

Breadth of the plot including the path =( 78 + 3 + 3)m = 84m

Now,

Area of plot PQRS including the path = Length×  Breadth

                                                              =( 131 × 84)

                                                              = 11004 $m^{2}$

Area of path = Area of plot PQRS − Area of plot ABCD

                     =  11004 - 9750

                     = 1254 $m^{2}$

Cost of gravelling =Rs.75 per $m^{2}$

Cost of gravelling the whole path = Rs.( 1254×75 ) = Rs.94050

Hence, cost of gravelling the path is Rs.94050.

Answer 2

From the given question the correct answer is:

the cost of gravelling the path is Rs.94050.

the area of the path is 1254

Given :

Length of the plot = 125 m

Breadth of the plot = 78 m

To find:

Area of path

the cost of gravelling

Concept used:

Area of path = Area of plot PQRS − Area of plot ABCD

Area of plot ABCD = Length × Breadth

                              = 125×78

                              = 9750  $m^{2}$

Length of the plot including the path = ( 125 + 3 + 3)m = 131m

Breadth of the plot including the path =( 78 + 3 + 3)m = 84m

Now,

Area of plot PQRS including the path = Length×  Breadth

                                                             =( 131 × 84)

                                                             = 11004$m^{2}$  

Area of path = Area of plot PQRS − Area of plot ABCD

                    =  11004 - 9750

                   = 1254$m^{2}$

Cost of gravelling =Rs.75 per  $m^{2}$

Cost of gravelling the whole path = Rs.( 1254×75 ) = Rs.94050

thus, cost of gravelling the path is Rs.94050.