Question

the least number of square slabs that can be fitted in a room 10.5 m long and 3m wide, is​

Answer 1

Solution -

We have,

• Length of the room = 10.5m
• Width of the room = 3m

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Now, let us find the total area of the room.

Since, room is in the shape of rectangle. Therefore, area of the room is given as :-

$\large{\bf{\longmapsto{\boxed{\pink{Area = Length \times Breadth}}}}}$

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$\tt\dashrightarrow{Area_{(Room)} = 10.5 \times 3}$

$\tt\dashrightarrow{Area_{(Room)} = 31.5\: m^2}$

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We have to find the dimensions of the square slab that can be fitted in the given room.

★ Dimension of slab = HCF (10.5, 3)

Therefore,

• Dimension = 1.5 m

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Now, we will find the area of each slab of side 1.5m. Area of a square is given as :-

$\large{\bf{\longmapsto{\boxed{\pink{Area = Side \times Side}}}}}$

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$\tt\dashrightarrow{Area_{(Slab)} = 1.5 \times 1.5}$

$\tt\dashrightarrow{Area_{(Slab)} = 2.25\: m^2}$

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Now, we have both the area of room and slab.

For finding the least number of slabs that can be fitted in the room, we divide the area of room by the area of slab.

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$\tt\longmapsto{Least\: number\: of\: slab = \dfrac{Area_{(Room)}}{Area_{(Slab)}}}$

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$\tt\longmapsto{Least\: number\: of\: slab = \dfrac{31.5}{2.25}}$

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$\bf\longmapsto{Least\: number\: of\: slab = 14}$

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Hence,

• The least number of square slabs that can be fitted in the room is 14.

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Answer 2

Answer:

Length =10.5m

Breadth =3m

Area of rectangle= L*B

Area= 10.5 * 3 = 31.5m