Question

A hall is $6m$ long and $10m$ wide. It is to be paved with equal share tiles. Find the least number of tiles which will exactly cover the floor.

Answer 1

We are assuming that the tiles are square and have area $a^2$ means every tiles is of side "$a$" square -

Now we take $m_1$ tiles along the $10m$ side

So, $a=\frac{10}{m_1}$ ..... $\left(1\right)$

Now we take $m_2$ tiles along the $6m$ side

$\Rightarrow$ $a=\frac{6}{m_2}$ ..... $\left(2\right)$

Total no of tiles $=m_1\times m_2$

Now equation $\left(1\right)$ and equation $\left(2\right)$ should be equal

So, $\frac{10}{m_1}=$ $\frac{6}{m_2}$

By solving this equation we get, $\frac{m_1}{m_2}$ = $\frac{5}{3}$

Now know that we want least no of tiles and $\frac{m_1}{m_2}$ = $\frac{5}{3}$

It will be minimum when $m_1=5$ and $m_2=3$

Total no of tiles $=m_1\times m_2$ = $5\times 3$

So the least no. of tiles that will cover the floor area will be $15$.