Question

Длина прямоугольного параллелепипеда в 2 раза больше ширины и на 10 см меньше высоты. Найти обьем прямоугольного параллелепипеда, если сумма длин всех его ребер = 160 см.

Answer 1

Ширина x см, длина 2x см, высота 2x+10 см, в сумме 160 см.
Каждое ребро в фигуре встречается 4 раза.
4*(x+2x+2x+10) = 160
4*(5x+10) = 160
20x+40 = 160
20x = 120
x = 6 см - ширина.
6*2 = 12 см - длина
12+10 = 22 см - высота.
Объём V = 6*12*22 = 1584 куб.см.

Answer 2

Problem Analysis

We are given the following information about a rectangular parallelepiped: - The length is twice the width. - The length is 10 cm less than the height. - The sum of all the lengths of the parallelepiped is 160 cm.

We need to find the volume of the rectangular parallelepiped.

Solution

Let's assign variables to the dimensions of the parallelepiped: - Let l be the length. - Let w be the width. - Let h be the height.

From the given information, we can write the following equations: 1. The length is twice the width: l = 2w. 2. The length is 10 cm less than the height: l = h - 10. 3. The sum of all the lengths is 160 cm: 2l + 2w + 2h = 160.

We can solve this system of equations to find the values of l, w, and h.

Substituting equation 1 into equation 2, we get: 2w = h - 10.

Substituting equation 1 into equation 3, we get: 4w + 2h = 160.

Now we have a system of two equations with two variables. We can solve this system to find the values of w and h.

Let's solve the system of equations:

2w = h - 10 (Equation A)

4w + 2h = 160 (Equation B)

From Equation A, we can express h in terms of w: h = 2w + 10.

Substituting this value of h into Equation B, we get: 4w + 2(2w + 10) = 160.

Simplifying the equation: 4w + 4w + 20 = 160.

Combining like terms: 8w + 20 = 160.

Subtracting 20 from both sides: 8w = 140.

Dividing both sides by 8: w = 17.5.

Substituting this value of w into Equation A, we can find h: h = 2(17.5) + 10 = 45.

Now that we have the values of w and h, we can find l using Equation 1: l = 2w = 2(17.5) = 35.

Therefore, the dimensions of the rectangular parallelepiped are: - Length (l) = 35 cm - Width (w) = 17.5 cm - Height (h) = 45 cm.

Calculating the Volume

The volume (V) of a rectangular parallelepiped is given by the formula: V = lwh.

Substituting the values we found, we get: V = 35 * 17.5 * 45.

Calculating the volume: V = 33075 cm³.

Therefore, the volume of the rectangular parallelepiped is 33075 cm³.

Answer

The volume of the rectangular parallelepiped is 33075 cm³.