Question

A mason has to fit a bathroom with square marble tiles filled of the largest possible size. The size of bathroom is \[10 \times 8{\text{ }}feet.\] What would be the size of the tiles in inches that has to be cut and how many such tiles are required?

Answer 1

Hint: To solve this question, we will start with converting the given values in inches. Then we will take H.C.F. of it, with that we will get the measurements of tiles. And then we will find the number of tiles required for it by using the suitable formula.

Complete step-by-step answer:
We have been given the size of bathroom i.e., \[10 \times 8{\text{ }}feet.\]
We know that, \[1{\text{ }}feet{\text{ }} = {\text{ }}12{\text{ }}inches\]
So, \[10{\text{ }}feet{\text{ }} = {\text{ }}10 \times 12{\text{ }} = {\text{ }}120{\text{ }}inches\]
And, \[8{\text{ }}feet{\text{ }} = {\text{ }}8 \times 12{\text{ }} = {\text{ }}96{\text{ }}inches\]
Now, we need to find the size of the square marble tiles in inches that has to be cut. For that we will take H.C.F. of \[\left( {120,96} \right).\]
\[\begin{array}{*{20}{l}}
  {120{\text{ }} = {\text{ }}2 \times 2 \times 2 \times 3 \times 5 = {2^3} \times 3 \times 5} \\
  {96 = {\text{ }}2 \times 2 \times 2 \times 2 \times 2 \times 3 = {2^5} \times 3} \\
  {HCF{\text{ }}\left( {120,96} \right){\text{ }} = {2^3} \times 3{\text{ }} = {\text{ }}24}
\end{array}\]
Thus, the size of the square marble tiles is \[24{\text{ }}inches.\]
Now, we need to find how many such tiles are required. For that we use the formula below mentioned.
Number of tiles \[ = \] $\dfrac{{{\text{area }}of{\text{ bathroom}}}}{{{\text{area }}of{\text{ tiles}}}}$
$ = \dfrac{{120 \times 96}}{{24 \times 24}}$
$ = 20$ tiles.
Thus, the size of the square marble tiles is \[24{\text{ }}inches,\] and \[20\] such tiles are required to fit the bathroom.

Note: Here, we took HCF to find the size of the square marble tiles, because in the question it was mentioned to find the largest possible size of tiles. HCF represents the highest possible tile and from that we can calculate the number of tiles required for the bathroom.