Question

Сумма длин всех рёбер прямоугольного параллелепипеда равна 376см.Найдите его измерения если известно что длина параллелепипеда втрое больше ширины а ширина на 14см меньше его высоты Составьте уравнение и решите задачу.помогите пожалуйста не могу решить эту задачу

Answer 1

Пусть длина параллелепипеда равна L, ширина равна W, а высота равна H.

Из условия задачи известно, что длина параллелепипеда втрое больше ширины, то есть L = 3W. Также известно, что ширина на 14 см меньше его высоты, то есть W = H - 14.

Сумма длин всех ребер прямоугольного параллелепипеда равна 376 см: 2L + 2W + 2H = 376.

Подставим значения L и W из предыдущих уравнений: 2(3W) + 2W + 2H =

Answer 2

Problem Analysis

We are given that the sum of the lengths of all the edges of a rectangular parallelepiped is 376 cm. We need to find the dimensions of the parallelepiped. We are also given that the length of the parallelepiped is three times the width, and the width is 14 cm less than the height.

Solution

Let's assume the width of the parallelepiped is x cm.

According to the given information, the length of the parallelepiped is three times the width, so the length would be 3x cm.

The width is also 14 cm less than the height, so the height would be x + 14 cm.

To find the sum of the lengths of all the edges, we need to consider all the edges of the parallelepiped. A rectangular parallelepiped has 12 edges, and each edge is counted twice (once for each adjacent face). So, the sum of the lengths of all the edges can be calculated as follows:

Sum of lengths of all edges = 2(length + width + height)

Substituting the given values, we have:

2(3x + x + (x + 14)) = 376

Simplifying the equation:

2(5x + 14) = 376
10x + 28 = 376
10x = 376 - 28
10x = 348
x = 348 / 10
x = 34.8

Therefore, the width of the parallelepiped is approximately 34.8 cm.

Using this value, we can find the length and height:

Length = 3x = 3 * 34.8 = 104.4 cm
Height = x + 14 = 34.8 + 14 = 48.8 cm

Therefore, the dimensions of the parallelepiped are approximately: - Width: 34.8 cm - Length: 104.4 cm - Height: 48.8 cm

Please note that the dimensions are approximate due to rounding.

Conclusion

The dimensions of the rectangular parallelepiped are approximately: - Width: 34.8 cm - Length: 104.4 cm - Height: 48.8 cm

I hope this helps! Let me know if you have any further questions.