Question

ПОМОГИТЕ ПОЖАЛУЙСТА На странице книги печатный текст должен занимать 432 см^2. Поля сверху и снизу должны быть по 2 см, а справа и слева по 1,5 см. Вычислить самые экономичные размеры бумаги

Answer 1

Ответ:

144

Пошаговое объяснение:

Найдем объем поля:

S=2*1,5=3

432/3=144

Answer 2

Calculating the Most Economical Paper Size

To calculate the most economical paper size for a book page with specific margins, we need to determine the dimensions of the printed text area and then find a paper size that can accommodate it.

Given: - Printed text area: 432 cm^2 - Top and bottom margins: 2 cm each - Left and right margins: 1.5 cm each

To calculate the dimensions of the printed text area, we subtract the margins from the total page dimensions.

Let's denote the width of the printed text area as W and the height as H.

The width of the printed text area can be calculated as follows: W = Total page width - Left margin - Right margin

The height of the printed text area can be calculated as follows: H = Total page height - Top margin - Bottom margin

Substituting the given values: W = Total page width - 1.5 cm - 1.5 cm H = Total page height - 2 cm - 2 cm

To find the most economical paper size, we need to find the dimensions that satisfy the equation: W * H = 432 cm^2

Let's solve this equation to find the dimensions of the printed text area.

Solution:

Substituting the calculated values into the equation, we have: (Total page width - 1.5 cm - 1.5 cm) * (Total page height - 2 cm - 2 cm) = 432 cm^2

Simplifying the equation, we get: (Total page width - 3 cm) * (Total page height - 4 cm) = 432 cm^2

To find the most economical paper size, we need to find the factors of 432 cm^2 and check if any combination satisfies the equation.

The factors of 432 cm^2 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432

Let's check each factor combination to find the dimensions that satisfy the equation.

1. Factor combination: 1 cm * 432 cm - Does not satisfy the equation.

2. Factor combination: 2 cm * 216 cm - Does not satisfy the equation.

3. Factor combination: 3 cm * 144 cm - Does not satisfy the equation.

4. Factor combination: 4 cm * 108 cm - Does not satisfy the equation.

5. Factor combination: 6 cm * 72 cm - Does not satisfy the equation.

6. Factor combination: 8 cm * 54 cm - Does not satisfy the equation.

7. Factor combination: 9 cm * 48 cm - Does not satisfy the equation.

8. Factor combination: 12 cm * 36 cm - Does not satisfy the equation.

9. Factor combination: 16 cm * 27 cm - Does not satisfy the equation.

10. Factor combination: 18 cm * 24 cm - Does not satisfy the equation.

11. Factor combination: 24 cm * 18 cm - Does not satisfy the equation.

12. Factor combination: 27 cm * 16 cm - Does not satisfy the equation.

13. Factor combination: 36 cm * 12 cm - Does not satisfy the equation.

14. Factor combination: 48 cm * 9 cm - Does not satisfy the equation.

15. Factor combination: 54 cm * 8 cm - Does not satisfy the equation.

16. Factor combination: 72 cm * 6 cm - Does not satisfy the equation.

17. Factor combination: 108 cm * 4 cm - Does not satisfy the equation.

18. Factor combination: 144 cm * 3 cm - Does not satisfy the equation.

19. Factor combination: 216 cm * 2 cm - Does not satisfy the equation.

20. Factor combination: 432 cm * 1 cm - Does not satisfy the equation.

After checking all the factor combinations, we can conclude that there are no dimensions that satisfy the equation W * H = 432 cm^2.

Therefore, it is not possible to find the most economical paper size that can accommodate a printed text area of 432 cm^2 with the given margins.

Please note that the calculations above assume a rectangular printed text area. If the printed text area has a different shape, the calculations may vary.

Let me know if there's anything else I can help you with!