question_answer 30)

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 Firstly, find the area of one tile and rectangular region separately. Then Area of rectangular region Required number of tiles \[=\frac{\text{Area}\,\text{of}\,\text{rectangular}\,\text{region}}{\text{Area}\,\text{of}\,\text{one}\,\text{tile}}\]

Answer:

Given, length of a tile = 12 cm and breadth of a tile = 5 cm \[\therefore \]Area of one tile = Length x Breadth =12 cm \[\times \] 5 cm = 60 sq cm Here, length of the rectangular region = 100 cm and breadth of the rectangular region = 144 cm \[\therefore \]Area of the rectangular region = Length \[\times \] Breadth \[=100cm\times 144cm=14400sqcm\] Now, number of required tiles \[=\frac{\text{Area of the rectangular region}}{\text{Area of the one tile}}\] \[\text{=}\frac{14400}{60}=240\] 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 of the rectangular region = Length x Breadth \[=70cm\times 36cm=2520sqcm\] Now, number of the required tiles \[\text{=}\frac{\text{Area of the rectangular region}}{\text{Area of the one tile}}\] \[\text{=}\frac{2520}{60}=42\] Hence, the number of the required tiles is 42.