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

Explanation:

Cost of polishing = Rs. 810

Step-by-step explanation:

\sf\red{given :-}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 :-}tofind:−

The total cost of polishing all the tiles

\sf\green{solution :-}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}}}

Areaofarhombus=

2

d

1

×d

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