question_answer

How many tiles whose length and breadth are 12 cm and 5 cm respectively will be needed to fit in a rectangular region whose length and breadth are respectively.

(a) 100 cm and 144 cm

(b) 70 cm and 36 cm.

Answer:

Given, length of a tile = 12 cm and breadth of a tile = 5cm

\[\therefore \] Area of one tile = Length \[\times \]Breadth

\[=12\text{ }cm\times 5\text{ }cm\]

\[=60\text{ }sq\text{ }cm\]

(a) Here, length of the rectangular region = 100 cm

and breadth of the rectangular region = 144 cm

\[\therefore \]  Area or the rectangular region

= Length \[\times \] Breadth

\[=100\text{ }cm\times 144\text{ }cm\]

\[=14400\text{ }sq\text{ }cm\]

Now, number or required tiles

\[\text{=}\frac{\text{Area}\,\,\text{of}\,\,\text{the}\,\,\text{rectangular}\,\,\text{region}}{\text{Area}\,\,\text{of}\,\,\text{the}\,\,\text{one}\,\,\text{tile}}\]

\[\text{=}\frac{14400}{60}=240\]

Hence, the number of required tiles is 240.

(b) Given, length of the rectangular region = 70 cm

and breadth of the rectangular region = 36 cm

\[\therefore \] Area or the rectangular region

= Length \[\times \] Breadth

\[=70\text{ }cm\times 36\text{ }cm=2520\text{ }sq\text{ }cm\]

Now, number or required tiles

\[\text{=}\frac{\text{Area}\,\,\text{of}\,\,\text{the}\,\,\text{rectangular}\,\,\text{region}}{\text{Area}\,\,\text{of}\,\,\text{the}\,\,\text{one}\,\,\text{tile}}\]

\[=\frac{2520}{60}=42\]

Hence, the number of required tiles is 42.