Question

The floor of a building consists of 3000 tiles which are rhombus shaped. The diagonals of each of the tiles are 45 cm and 30 cm. Find the cost of polishing the floor, if cost per sq. m is Rs. 250.

Answer 1

Hint: Find the area of one tile using the formula for area of the rhombus using its value of diagonals. Then find the area of the floor of the building by multiplying the area of each tile by 3000. Then find the total cost of polishing the floor by multiplying total area by the cost per sq. m.

Complete step-by-step answer:

The floor of the building has 3000 tiles and each tile is in the shape of the rhombus. The diagonals of the rhombus are 45 cm and 30 cm respectively.

We know that the area of the rhombus with diagonals of length p and q is given as follows:
\[A = \dfrac{1}{2}pq\]
Using this formula, the area of the rhombus with diagonals 45 cm and 30 cm is given as follows:
\[A = \dfrac{1}{2}(45)(30)\]
Simplifying, we have:
\[A = 675c{m^2}\]
Total area of the floor of the building is the area of each tile multiplied with 3000.
Total area = \[3000 \times 675\]
Total area = \[2025000c{m^2}\]
Converting into sq. m by dividing with \[{10^4}c{m^2}/{m^2}\], we have:
Total area = \[\dfrac{{2025000c{m^2}}}{{{{10}^4}c{m^2}/{m^2}}}\]
Total area = \[202.5{m^2}\]
Total cost of polishing the floor is given by:
Total cost = Total area \[ \times \] Cost per sq. m
Total cost = \[202.5 \times 250\]
Total cost = \[Rs.50625\]
Hence, the total cost is Rs. 50625.

Note: You might forget to convert the total area into sq. metres before finding the total cost, then, you will get a wrong answer. The cost is given per sq. metres and hence, the area also should be in sq. metres.