Question

How many tiles whose length and breadth are 12 cm and 5 cm respectively will be
needed to fit in a rectangular region whose length and breadth are respectively :
i. 100 cm and 144 cm
ii. 70 cm and 36 cm
​

Answer 1

Answer:

it may be 12 from my guess

Answer 2

Let's solve both the questions one by one!

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$\underline{\boxed{\mathfrak{Answer \: i:-}}}$

• 240 tiles will be needed to fit in a rectangular region whose length and breadth are 100 cm and 144 cm respectively.

Given :-

• Length of the tile = 12 cm.

• Breadth of the tile = 5 cm.

• Length of the rectangular region = 100 cm.

• Breadth of the rectangular region = 144 cm.

To find :-

• The number of tiles needed to fit in the rectangular region.

Step-by-step explanation :-

• To find the number of tiles which can fit in a rectangular region of length 100 cm and breadth 144 cm, let's find the area of each tile first.

• The tile is in the shape of a rectangle, since it's length and breadth is given.

• So, to find the area of the tile, we are going to use the formula required for finding the area of a rectangle.

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Calculations :-

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth.}}$

Here,

• Length of the tile = 12 cm.

• Breadth of the tile = 5 cm.

Hence,

$\boxed{\tt Area\: of\: each\: tile = 12 \times 5}$

Multiplying the numbers,

$\overline{\boxed{\tt Area \: of \:each \:tile = 60.}}$

• Therefore, the area of each tile = 60 cm².

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• Now, since we know the area of each tile, therefore let's find the area of the rectangular region.

• The region is in the shape of a rectangle, since it's a rectangular region.

• So, to find the area of the region, we are going to use the formula required for finding the area of a rectangle.

---------------------------

As given above,

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth.}}$

Here,

• Length of the region = 100 cm.

• Breadth of the region = 144 cm.

Hence,

$\boxed{\tt Area \: of \: the \: region = 100 \times 144}$

Multiplying the numbers,

$\underline{\fbox{\tt Area of the region = 14400.}}$

• Therefore, the area of the rectangular region = 14400 cm².

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Now,

$\underline{\boxed{\sf No. \: of\: tiles \:needed = \dfrac{Area\: of \: the \: region}{Area \:of \:each \: tile}}}$

Substituting the values in the given formula,

$\boxed{\tt No. \: of\: tiles \:needed = \dfrac{14400}{60}}$

Dividing 14400 by 60,

$\underline{\boxed{\tt No. \: of \: tiles \: needed = 240.}}$

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$\underline{\boxed{\mathfrak{Answer \: ii :-}}}$

• 42 tiles will be needed to fit in a rectangular region whose length and breadth are 70 cm and 36 cm respectively.

Given :-

• Length of each tile = 12 cm.

• Breadth of each tile = 5 cm.

• Length of the rectangular region = 70 cm.

• Breadth of the rectangular region = 36 cm.

To find :-

• The number of tiles needed to fit in the rectangular region.

Step-by-step explanation :-

• To find the number of tiles which can fit in a rectangular region of length 100 cm and breadth 144 cm, let's find the area of each tile first.

• The tile is in the shape of a rectangle, since it's length and breadth is given.

• So, to find the area of the tile, we are going to use the formula required for finding the area of a rectangle.

---------------------------

Calculations :-

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth.}}$

Here,

• Length of the tile = 12 cm.

• Breadth of the tile = 5 cm.

Hence,

$\boxed{\tt Area\: of\: each\: tile = 12 \times 5}$

Multiplying the numbers,

$\overline{\boxed{\tt Area \: of \:each \:tile = 60.}}$

• Therefore, the area of each tile = 60 cm².

---------------------------

• Now, since we know the area of each tile, therefore let's find the area of the rectangular region.

• The region is in the shape of a rectangle, since it's a rectangular region.

• So, to find the area of the region, we are going to use the formula required for finding the area of a rectangle.

---------------------------

As given above,

$\underline{\boxed{\sf Area \: of \: a \: rectangle = Length \times Breadth.}}$

Here,

• Length of the region = 70 cm.

• Breadth of the region = 36 cm.

Hence,

$\boxed{\tt Area \: of \: the \: region = 70 \times 36}$

Multiplying the numbers,

$\underline{\fbox{\tt Area of the region = 2520.}}$

• Therefore, the area of the rectangular region = 2520 cm².

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Now,

$\underline{\boxed{\sf No. \: of\: tiles \:needed = \dfrac{Area\: of\: region}{Area \:of \:each \: tile}}}$

Substituting the values in the given formula,

$\boxed{\tt No.\: of\: tiles \:needed = \dfrac{2520}{60}}$

Dividing 14400 by 60,

$\underline{\boxed{\tt No. \: of \: tiles \: needed = 42.}}$

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