Question

how many tiles each measuring 4m by 2.5 m are required to cover a rectangular room whose lenght and breadth are 45 m and 22m Find the cost of tiles at Rs 35 per tile. please give step by step explanation​

Answer 1

Answer

• Number of tiles required to cover the room = 99
• Cost of tiles = Rs. 3465

Explanation :-

Given

• Dimensions of the tiles :-

• Length of the tiles = 4 m
• Breadth of the tiles = 2.5 m

• Dimensions of the rectangular room :-

• Length of the rectangular room = 45 m
• Breadth of the rectangular room = 22 m

To find

• Number of tiles required to cover the room
• Cost of tiles

Knowledge required :-

• Formula to calculate area of rectangle :-

⠀⠀⠀Area of rectangle = l × b

where,

• l = length of the rectangle
• b = breadth of the rectangle

~Understanding the concept ::

To find the number of tiles required to cover the room.. Firstly, we will find the area of the room and area of each tile using the formula of area of rectangle. Then we will divide the area of room by area of each tile. From there we will get the number of tiles required to cover the room.

Now, to find the cost of tiles at the rate of rs. 35. We will multiply the no. of tiles to cover the room by the rate.

Solution

Area of room :-

⠀⠀⠀⇒ Area of room = l × b

⠀⠀⠀⇒ Area = 45 × 22

⠀⠀⠀⇒ Area = 990

Area of the room = 990 m²

Area of each tile :-

⠀⠀⠀⇒ Area of each tile = l × b

⠀⠀⠀⇒ Area = 4 × 2.5

⠀⠀⠀⇒ Area = 10

Area of each tile = 10 m²

Number of tiles required to cover the room = Area of room ÷ Area of each tile

⠀⠀⠀⇒ No. of tiles required to cover the room = 990 ÷ 10

⠀⠀⠀⇒ 990/10

⠀⠀⠀⇒ 99

Number of tiles required to cover the room = 99 ★

Cost of tiles = No. of tiles × Rate

⠀⠀⠀⇒ Cost of tiles = 99 × 35

⠀⠀⠀⇒ Cost of tiles = 3465

Cost of tiles = Rs. 3465 ★

Answer 2

Need To find:-

• Number of tiles required to cover the room
• Cost of tiles.

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According to the question, we are given length of the tiles is 4 m & breadth of the tiles is 2.5 m.And also this question provided us information about dimensions of the rectangular room. It seems that length of the rectangular room is 45 m & breadth of the rectangular room is 22 m.For solving this question, we need to know one formula :-

• Area of rectangle = l × b

Where, l means length of the rectangle and b means breadth of the rectangle.

At first, we have find the area of the room and area of each tile using the formula of area of rectangle.After that, we will number of tiles required to cover the room.

Calculation :-

$\implies { \sf{ \pmb{Area \: _{(Room)} = l \times b \: sq.units}}} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 45 \times 22} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline\pink{{990 \: {m}^{2}}} }$

Finding the area of a tile –

$\implies { \sf{ \pmb{Area \: _{(Tile)} = l \times b \: sq.units}}} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 \times 2.5} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline\pink{{10 \: {m}^{2}}} }$

Now,finding number of tiles required to cover the room :-

$\implies { \sf{ \dfrac{Area \: of \: room }{Area \: of \: a \: tile} }} \\ \\ \implies { \sf{ \dfrac{ \cancel{990}}{ \cancel{10}}}} \\ \\ \implies \underline{\boxed{ \tt{ \pmb{ \purple{99}}}}}$

$\implies { \sf{ \pmb{Cost \: _{(Tile)} = No \:of \:tiles \times Rate }}} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 99 \times 35} \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \underline\pink{{3465}} }$

$\\ \therefore \underline{ \sf{ \pmb{ \purple{99 \: tiles} \: are \: required \: to \: cover \: the \: room \: and \: cost \: of \: tiles \: will \: be \: \pink {Rs \: 3465 }.}}}$

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