Question

Длина прямоугольного параллелепипеда в2 раза больше ширины и на 10 см меньше высоты. Найти объём прямоугольного параллелепипеда, если сумма длин всех его рёбер равна 160 см

Answer 1

Х - длина
х : 2 - ширина
х + 10 - высота
4х + 4х:2 + (4х+10) = 160
12х : 2 + 10 = 160
12х : 2 = 160 -10
12х : 2 = 150
12х = 150 умножить на 2
12х = 300
х = 300 : 12
х = 25(см)
1) 25 : 2 = 12.5 ( см ) - ширина
2) 25 + 10 = 35 (см) - высота
3) 25 умножить на 12.5 умножить на 35 = 10937.5 (см 3)
ответ: 10937.5 см 3

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 = x cm - Length = 2x cm - Height = 2x + 10 cm

To find the volume, we use the formula: Volume = Length × Width × Height.

Substituting the given values, we have: Volume = (2x) × x × (2x + 10)

To find the sum of the lengths of all the edges, we use the formula: Sum of lengths of all edges = 4 × (Length + Width + Height).

Substituting the given values, we have: 160 = 4 × (2x + x + 2x + 10)

Now, let's solve the equation to find the value of x.

Calculation

160 = 4 × (2x + x + 2x + 10) 160 = 4 × (5x + 10) 160 = 20x + 40 20x = 120 x = 6

Now that we have the value of x, we can substitute it back into the volume formula to find the volume of the rectangular parallelepiped.

Volume = (2x) × x × (2x + 10) Volume = (2 × 6) × 6 × (2 × 6 + 10) Volume = 12 × 6 × (12 + 10) Volume = 12 × 6 × 22 Volume = 1584 cm³

Answer

The volume of the rectangular parallelepiped is 1584 cm³.