Through a rectangular field of length $90\ m$ and breadth $60\ m$, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is $3\ m$, find
$(i)$ the area covered by the roads.
$(ii)$ the cost of constructing the roads at the rate of $₹ 110\ per\ m^2$.
Length of the road along the length of the field$= 90\ m$
Breadth$= 3\ m$
Area of the road$= l\times b$
$=90m\times3m=270m^2$
Similarly, the area of the road parallel to the breadth of the field$=l\times b$
$=60\ m\times3\ m=180\ m^2$
Area of the common portion$=3\ m\times3\ m=9m^2$
$(i)$. Area of the two roads
$=270\ m^2+180\ m^2-9\ m^2$
$=450\ m^2-9\ m^2=441\ m^2$
$(ii)$. Cost of constructing the roads
$=Rs\ 110\times441=Rs\ 48,510$
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