Question

the floor of a building consists of 3000 tiles which are Rhombus shaped and each of its diagonal are 45 cm and 30 cm in length find the total cost of polishing the floor if the cost per metre square is 4 ​

Answer 1

$\huge\boxed{\fcolorbox{purple}{ink}{Answer}}$

Cost of polishing = Rs. 810

Step-by-step explanation:

$\sf\red{given :-}$

Diagonals of the rhombus = 45 cm and 30 cm

Total number of tiles = 300

Cost of polishing = Rs. 4 per m²

$\sf\blue{to\:find :-}$

The total cost of polishing all the tiles

$\sf\green{solution :-}$

First finding the area of a rhombus shaped tile.

Area of a rhombus is given by,

$\boxed{\tt\blue {Area\:of\:a\:rhombus=\dfrac{d_1\times d_2}{2}}}$

where d₁ is the first diagonal,

d₂ is the second diagonal

Substitute the data,

Area of the tile = (45 × 30)/2

⇒ 1350/2

⇒ 675 cm²

Hence the area of each tile is 675 cm².

Therefore,

Area of 3000 tiles = 3000 × Area of 1 tile

⇒ 3000 × 675

⇒ 2025000 cm² = 202.5 m²

Now the total cost of polishing is given by,

Cost of polishing = Area of the tiles × Rate per m²

⇒ 202.5 × 4

⇒ 810 rupees

Hence the total cost of polishing the floor is 810 rupees.

Answer 2

₹810 is the crt answer

Explanation:

Given,

Total Number of tiles used = 3000

Since tile is in the shape of rhombus and Diagonals are 45 cm and 30 cm

Thus,

d1 = 30 cm

d2 = 45 cm

Area of one tile Area of rhombus

= 1/2×x×d1×d2

1/2× 30 × 45

= 15 x 45

= 675 cm

Area of 3000 tiles = 3000 x Area of 1 tile

= 3000 x 675

= 2025000 cm

Now, we need to find cost.

Since cost is given per m²

We need to convert the area into m²

Area = 2025000 cm²

2025000 x (1/100) ² m²

2025000 / 10000 m²

= 202.5 m²

Now,

Cost of Polishing 1 m = 4

Cost of Publishing 202.5 m2 = 4 x 202.5

= 4×2025/10

=4 x 405/2

= 810

Total cost of polishing the floor = Rs 810

hope it helps you...