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(C) To find the least number of square slabs,we must find the side of the largest possible square tile that can fit perfectly into the dimensions of t

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(C) To find the least number of square slabs,we must find the side of the largest possible square tile that can fit perfectly into the dimensions of the room.$1$. The side of the largest square tile is the Greatest Common Measure $(GCM)$ or Highest Common Factor $(HCF)$ of the length $(10.5 	ext{ m})$ and the breadth $(3 	ext{ m})$.$2$. Convert $10.5$ and $3$ to a common unit or fraction: $10.5 = \frac{21}{2}$ and $3 = \frac{6}{2}$.$3$. The $HCF$ of $\frac{21}{2}$ and $\frac{6}{2}$ is $\frac{	ext{HCF}(21, 6)}{	ext{LCM}(2, 2)} = \frac{3}{2} = 1.5 	ext{ m}$.$4$. The area of the room is $10.5 	imes 3 = 31.5 	ext{ m}^2$.$5$. The area of one square tile is $1.5 	imes 1.5 = 2.25 	ext{ m}^2$.$6$. The number of tiles needed = $\frac{	ext{Area of room}}{	ext{Area of one tile}} = \frac{31.5}{2.25} = 14$.

The least number of square slabs that can be fitted in a room of $10.5 \text{ m}$ long and $3 \text{ m}$ wide is........?

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