To find the cost of carpeting the room, we need to calculate the area of the room and then determine how many meters of carpet we need to cover that area.
The room's dimensions are:
$\sf{\underline{Length = 13 m}}$
$\sf{\underline{Breadth = 9 m}}$
We can calculate the area of the room as:
$\sf\longrightarrow\:Area = Length \times Breadth$
$\sf\longrightarrow\:Area = 13m \times 9m$
$\sf\longrightarrow\:Area = 117m^2$
Since the carpet is 75 cm broad, we need to convert it into meters:
$\sf\longrightarrow\:1m = 100cm$
$\sf\longrightarrow\:75cm = \frac{75}{100m}$
$\sf\longrightarrow\:75cm = 0.75m$
So the width of the carpet in meters is 0.75m.
Now, we can calculate how many meters of carpet we need to cover the room:
$\sf\longrightarrow\:Length\ of\ carpet\ needed$
$\sf\\= Length\ of\ room = 13m$
$\sf\longrightarrow\:Breadth\ of\ carpet\ needed$
$\sf\:= Breadth\ of\ room + 2 \times Width\ of\ carpet$
$\sf\longrightarrow\:Breadth\ of\ carpet\ needed$
$\sf\:= 9m + 2\times 0.75m$
$\sf\longrightarrow\:Breadth\ of\ carpet\ needed$
$\sf\bigstar\:= 10.5m$
The total area of the carpet needed is:
$\sf\longrightarrow\:Area\ of\ carpet = Length\ of\ carpet$
$\sf\:needed \times Breadth\ of\ carpet\ needed$
$\sf\longrightarrow\:Area\ of\ carpet = 13m \times 10.5m$
$\sf\longrightarrow\:Area\ of\ carpet = 136.5m^2$
Now we can calculate the cost of the carpet:
$\sf\longrightarrow\:Cost\ of\ carpet = Cost\ per\ metre$
$\sf\:\times Length\ of\ carpet$
$\sf\longrightarrow\:Cost\ of\ carpet = ¥50/m \times 136.5m^2$
$\longrightarrow\bigstar\boxed{\textcolor{red}{\sf{Cost\ of\ carpet = ¥6,825}}}$
Therefore, the cost of carpeting the room with a carpet 75cm broad at ¥50 per metre is ¥6,825.
