Question

The floor of a building consists of $3000$ tiles which are rhombus-shaped and each of its diagonals are $45cm$ and $30cm$ in length. Find the total cost of polishing the floor, if the cost per $m^2$ is $Rs.4.$

Answer 1

Length of diagonals are, $d_1=45cmand{d}_2=30cm$

Step 1: Find the area of one tile and then the area of $3000$ tiles.

Area of one tile $=\frac{1}{2}\times d_1\times d_2$

$$\begin{gathered} =\frac{1}{2}\times 45\times 30 \\ =675c{m}^2 \end{gathered}$$

So, the area of one tile is $675c{m}^2$

The area of $3000$ tiles is $=675\times 3000$

$$\begin{gathered} =2025000c{m}^2 \\ =\frac{2025000}{10000}[\because 1m^2=10000c{m}^2] \\ =202.50m^2 \end{gathered}$$

Step 2: Find the cost of polishing the floor.

Cost of polishing the floor per sq. meter $=Rs.4$

Cost of polishing the floor per $202.50sq.meter=4\times 202.50=810$

Hence, the total cost of polishing the floor is $Rs.810.$