Question

в прямом параллелепипеде стороны основания 3 см и 6 см образуют угол 30 градусов, площадь полной поверхности 144 см в квадрате, найти боковое ребро

Answer 1

Объяснение:

см фото,,,,,,,,,,,,,,,,,,,,,,

Answer 2

Finding the lateral edge of a rectangular parallelepiped

To find the lateral edge of a rectangular parallelepiped, we need to use the given information about the dimensions of the base, the angle formed, and the total surface area.

Let's break down the problem step by step:

1. Given information: - The sides of the base of the parallelepiped are 3 cm and 6 cm. - The angle formed between these sides is 30 degrees. - The total surface area of the parallelepiped is 144 cm².

2. Finding the lateral edge: - The total surface area of a rectangular parallelepiped is given by the formula: 2(ab + bc + ac), where a, b, and c are the lengths of the sides of the parallelepiped. - In this case, we have the total surface area as 144 cm². So we can write the equation as: 2(3b + 6c + 18) = 144, where b and c are the lengths of the other two sides of the parallelepiped. - Simplifying the equation, we get: 3b + 6c + 18 = 72. - Rearranging the equation, we have: 3b + 6c = 54.

3. Using trigonometry to find the lengths of the other two sides: - We know that the angle formed between the sides of the base is 30 degrees. - Using trigonometry, we can write the following equations: - b = 3cos(30°) - c = 6sin(30°).

4. Substituting the values of b and c into the equation from step 2: - Substituting the values of b and c, we get: 3(3cos(30°)) + 6(6sin(30°)) = 54. - Simplifying the equation, we have: 9cos(30°) + 36sin(30°) = 54.

5. Solving the equation: - Using a calculator, we can find the values of cos(30°) and sin(30°): - cos(30°) ≈ 0.866 - sin(30°) ≈ 0.5. - Substituting these values into the equation, we get: 9(0.866) + 36(0.5) = 54. - Simplifying the equation, we have: 7.794 + 18 = 54. - Combining like terms, we get: 25.794 = 54. - Solving for the value of the lateral edge, we have: 25.794 = 54.

Therefore, the lateral edge of the rectangular parallelepiped is approximately 25.794 cm.

Please note that the search results provided by You.com did not contain relevant information for this specific problem. The solution was derived using mathematical principles and trigonometry.