Question

Периметр граней АВСД, АВ В1 А1 і АД Д1 А1 прямокутного паралелепіпеда АВСД А1 В1 С1 Д1 = 20м, 36м і 32м. знайдіть суму довжин усіх його ребер." >

Answer 1

Р(АВСД)=20см. Р(АВВ1А1)=36см, Р(АДД1А1)=32см. Обозначим измерения параллелепипеда(длины трех ребер, выходящих из одной вершины) а, b, c. Составим систему трех уравнений с тремя неизвестными: {(a+b)*2=20 (B+c)*2=36 (a+c)*2=32 {a+b=10 b+c=18 a+c=16 {a+b+b+c=10+18 a+c=16 {a+c+2b=28 a+c=16 16+2b=28 2b=12 b=6 a=4 c=12 6+4+12=22 Ответ:a+b+c=22см

Answer 2

Perimeter of the Edges of a Rectangular Parallelepiped

To find the sum of the lengths of all the edges of a rectangular parallelepiped, we need to calculate the perimeter of each face and add them together.

Let's assume that the lengths of the edges of the rectangular parallelepiped are as follows: - Length of edge AB = 20m - Length of edge BC = 36m - Length of edge CD = 32m

To calculate the perimeter of each face, we need to consider the edges that form that face. The rectangular parallelepiped has six faces, and each face is a rectangle.

The perimeter of a rectangle is given by the formula: Perimeter = 2 * (Length + Width).

Let's calculate the perimeter of each face:

1. Face ABCD: - Length = AB = 20m - Width = BC = 36m - Perimeter = 2 * (20m + 36m) = 2 * 56m = 112m

2. Face A1B1C1D1: - Length = AB = 20m - Width = BC = 36m - Perimeter = 2 * (20m + 36m) = 2 * 56m = 112m

3. Face ABA1A1: - Length = AB = 20m - Width = A1A1 = CD = 32m - Perimeter = 2 * (20m + 32m) = 2 * 52m = 104m

4. Face BCB1C1: - Length = BC = 36m - Width = B1C1 = AD = 20m - Perimeter = 2 * (36m + 20m) = 2 * 56m = 112m

5. Face CDC1D1: - Length = CD = 32m - Width = C1D1 = AB = 20m - Perimeter = 2 * (32m + 20m) = 2 * 52m = 104m

6. Face ADA1D1: - Length = AD = 20m - Width = A1D1 = BC = 36m - Perimeter = 2 * (20m + 36m) = 2 * 56m = 112m

Now, let's find the sum of the lengths of all the edges by adding the perimeters of each face:

Sum of lengths of all edges = Perimeter of ABCD + Perimeter of A1B1C1D1 + Perimeter of ABA1A1 + Perimeter of BCB1C1 + Perimeter of CDC1D1 + Perimeter of ADA1D1 = 112m + 112m + 104m + 112m + 104m + 112m = 656m

Therefore, the sum of the lengths of all the edges of the given rectangular parallelepiped is 656 meters.