Question

A rectangular room measuring 45 cm by 25 cm is to be tiled using square tiles. i) What is the largest size tile that can be used to tile the floor? ii) How many tiles are needed to tile the floor, without cutting?

Answer 1

$\large\underline{\sf{Solution-}}$

Dimensions of rectangular room

• Length of room = 45 cm

• Breadth of room = 25 cm

Now, it is given that rectangular room measuring 45 cm by 25 cm is to be tiled using square tiles.

So, edge of square tile = HCF (45, 25)

Calculations of HCF of 45 and 25

Prime factorization of 45 = 3 × 3 × 5

Prime factorization of 25 = 5 × 5

It implies, HCF (45, 25) = 5

So, it means, edge of square tile = 5 cm.

So, largest size of tile that can be used to tile the floor is 5 cm.

Let assume that n number of tiles are needed to tile the floor, without cutting.

$\rm \: n \times Area_{(tile)} = Area_{(Room)}$

$\rm \: n \times {(5)}^{2} = 45 \times 25$

$\rm \: n \times 25 = 45 \times 25$

$\rm\implies \:n \: = \: 45$

Hence, 45 number of tiles are needed to tile the floor, without cutting.

$\rule{190pt}{2pt}$

Formulae Used :-

$\boxed{ \rm{ \:Area_{(Rectangle)} = Length \times breadth \: }}$

$\boxed{ \rm{ \:Area_{(Square)} = {(side)}^{2} \: }}$

$\rule{190pt}{2pt}$

Additional information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

A rectangular room measuring 45 cm by 25 cm is to be tiled using square tiles. i) What is the largest size tile that can be used to tile the floor? Ii) How many tiles are needed to tile the floor, without cutting?

I think that you need to rewrite your question 45 cm = about 17.2 inches and 25 cm is about 9.8 inches.

Mathematically, tiles of 2.5 cm² or 5 cm² would not need to be cut.

Number of tiles? 180 * 2.5x2.5 or 45 * 5x5.

The smallest tiles that I’ve seen here are 1 cm² on paper-backed sheets

is how i would  answer this.