Question
A rectangular plot measures $125\ m$ by $78\ m$. It has gravel path 3m wide all around on the outside. Find the area of the path and the cost of gravelling it at $₹\ 75\ per\ m^2.$
✓
Answer
Length of the plot $= 125m$ Breath of the plot $= 78m$
Area of the plot $ABCD = (125 \times 78)m^2 = 9750m^2$
Length of the plot including the path $= (125 + 3 + 3)m = 131m$
Breath of the plot including the path $= (78 + 3 + 3)m = 84m$
Area of plot $PQRS$ including the path $= (131 \times 84)m^2\ 11004m^2$
Area of path = Area of plot $PQRS$ Area of plot $ABCD = (11004 \times 9750)m^2 = 1254m^2$
Cost of gravelling $= ₹\ 75\ per\ m^2$
$\therefore$ Cost of gravelling the whole path $= ₹ (1254 \times 75) = ₹ 94050$
Hence, cost of gravelling the path $= ₹ 94050.$
Area of the plot $ABCD = (125 \times 78)m^2 = 9750m^2$
Length of the plot including the path $= (125 + 3 + 3)m = 131m$
Breath of the plot including the path $= (78 + 3 + 3)m = 84m$
Area of plot $PQRS$ including the path $= (131 \times 84)m^2\ 11004m^2$
Area of path = Area of plot $PQRS$ Area of plot $ABCD = (11004 \times 9750)m^2 = 1254m^2$
Cost of gravelling $= ₹\ 75\ per\ m^2$
$\therefore$ Cost of gravelling the whole path $= ₹ (1254 \times 75) = ₹ 94050$
Hence, cost of gravelling the path $= ₹ 94050.$
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