Question

помогите решить задачу по геометрии. Диагональ прямоугольного параллелепипеда равна 3 см, а его измерения относятся как 1:2:2. Определить ребра параллелепипеда. Заранее большое спасибо.

Answer 1

ребра паралелепипида=12,по измерениям = диагональ

Answer 2

Problem Analysis

To solve this geometry problem, we need to find the dimensions of a rectangular parallelepiped (also known as a rectangular prism) given that its diagonal is 3 cm and its dimensions are in the ratio of 1:2:2.

Solution

Let's assume the dimensions of the rectangular parallelepiped are x, 2x, and 2x.

To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangular parallelepiped is the hypotenuse, and the sides of the parallelepiped are the other two sides of the right-angled triangle.

Using the Pythagorean theorem, we can write the equation:

x^2 + (2x)^2 + (2x)^2 = (3 cm)^2

Simplifying the equation:

x^2 + 4x^2 + 4x^2 = 9 cm^2

9x^2 = 9 cm^2

Dividing both sides of the equation by 9:

x^2 = 1 cm^2

Taking the square root of both sides:

x = 1 cm

Therefore, the dimensions of the rectangular parallelepiped are:

Length: x = 1 cm

Width: 2x = 2 cm

Height: 2x = 2 cm

So, the edges of the parallelepiped are 1 cm, 2 cm, and 2 cm.

Conclusion

The edges of the rectangular parallelepiped are 1 cm, 2 cm, and 2 cm.