Question

Длина прямоугольного параллелепипеда в 2 раза больше ширины и на 10 см меньше высоты .Найдите объём прямоугольного параллелепипеда ,если сумма длин всех его рёбер равна 160 см.

Answer 1

Х-ширина,2х-длина,2х+10-высота
4(х+2х+2х+10)=160
5х+10=40
5х=30
х=6-ширина
6*2=12-длина
12+10=22-высота
V=6*12*22=1584см³

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 the lengths of all its edges is 160 cm.

We need to find the volume of the rectangular parallelepiped.

Solution

Let's assume: - Width = w cm - Length = 2w cm (twice the width) - Height = 2w + 10 cm (10 cm more than the length)

To find the volume, we multiply the length, width, and height of the parallelepiped.

Calculation

The sum of the lengths of all the edges is given as 160 cm. Each edge has two equal sides, so the sum of the lengths of all the edges is equal to 4 times the sum of the lengths of the three sides.

Let's calculate the sum of the lengths of the three sides: - Length + Width + Height = 2w + w + (2w + 10) = 5w + 10

According to the problem, the sum of the lengths of all the edges is 160 cm, so we can write the equation: 4 * (5w + 10) = 160

Simplifying the equation: 20w + 40 = 160 20w = 120 w = 6

Now that we have the width, we can calculate the length and height: - Length = 2w = 2 * 6 = 12 cm - Height = 2w + 10 = 2 * 6 + 10 = 22 cm

Finally, we can calculate the volume: Volume = Length * Width * Height = 12 * 6 * 22 = 1584 cubic cm.

Therefore, the volume of the rectangular parallelepiped is 1584 cubic cm.

Answer

The volume of the rectangular parallelepiped is 1584 cubic cm.