Question

2. Прямоугольный участок размером 72 х 35 покрывается плитками 4x7. Можно ли покрыть этот участок ровными рядами плитками 8 x 5? 7 x 16? Обоснуйте свой ответ. Если да, то сколько плиток для этого потребуется? [4]

Answer 1

Площадь участка 72*35=2520 ед²

Площадь плитки 7*4=28 ед²

Таких плиток потребуется 2520:28=90 шт.

Если площадь плитки 8*5=40 ед², то потребуется 2520:40=63 плиток.

Если площадь плитки 7*16=112 ед², то потребуется

2520:112=22,5 плиток, т.е. ровный ряд не получится.

Answer 2

Can the rectangular area of 72 x 35 be covered with tiles of 4 x 7, 8 x 5, and 7 x 16?

To determine if the rectangular area of 72 x 35 can be covered with tiles of different dimensions, we can calculate the number of tiles needed for each case and compare it with the total number of tiles available.

1. Covering with 4 x 7 tiles: - The area of each 4 x 7 tile is 4 * 7 = 28 square units. - The total area to be covered is 72 * 35 = 2520 square units. - Therefore, the number of 4 x 7 tiles needed = Total area / Area of each tile = 2520 / 28 = 90 tiles.

2. Covering with 8 x 5 tiles: - The area of each 8 x 5 tile is 8 * 5 = 40 square units. - The total area to be covered is 72 * 35 = 2520 square units. - Therefore, the number of 8 x 5 tiles needed = Total area / Area of each tile = 2520 / 40 = 63 tiles.

3. Covering with 7 x 16 tiles: - The area of each 7 x 16 tile is 7 * 16 = 112 square units. - The total area to be covered is 72 * 35 = 2520 square units. - Therefore, the number of 7 x 16 tiles needed = Total area / Area of each tile = 2520 / 112 = 22.5 tiles.

Conclusion:

Based on the calculations, it is possible to cover the rectangular area of 72 x 35 with all three types of tiles. However, the number of tiles required varies for each case: - For 4 x 7 tiles: 90 tiles are needed. - For 8 x 5 tiles: 63 tiles are needed. - For 7 x 16 tiles: 22.5 tiles are needed.

It's important to note that the number of 7 x 16 tiles needed is not a whole number, indicating that this tile size may not be the most efficient option for covering the given area.