How many tiles whose length and breadth are $ 12 \mathrm{~cm} $ and $ 5 \mathrm{~cm} $ respectively will be needed to fit in a rectangular region whose length and breadth are respectively:
(a) $ 100 \mathrm{~cm} $ and $ 144 \mathrm{~cm} $
(b) $ 70 \mathrm{~cm} $ and $ 36 \mathrm{~cm} $.

To do:

We have to find the number of tiles needed to fit in the rectangular regions whose length and breadth are respectively:

(a) $100\ cm$ and $144\ cm$

(b) $70\ cm$ and $36\ cm$.

Solution:

We know that,

The area of a rectangle with length '$l$' and breadth '$b$' is $l \times b$.

The area of one tile $= 12\ cm\times5\ cm$

$= 60\ cm^2$

(a) The area of the rectangular region $=100\ cm\times144\ cm$

$= 14400\ cm^2$

We get the number of tiles by dividing the area of the rectangular region by the area of one tile.

The number of tiles required $= \frac{14400\ cm^2\ cm}{60\ cm^2}$

$=240$

The number of tiles needed to fit in the rectangular region is $240$.  

(b) The area of the rectangular region $=70\ cm\times36\ cm$

$= 2520\ cm^2$

We get the number of tiles by dividing the area of the rectangular region from the area of one tile.

The number of tiles required $= \frac{2520\ cm^2\ cm}{60\ cm^2}$

$=42$

The number of tiles needed to fit in the rectangular region is $42$.