Measurements of a rectangular parallelepiped are 1: 2: 4 Determine the measurements

Measurements of a rectangular parallelepiped are 1: 2: 4 Determine the measurements of a rectangular parallelepiped if its volume is 1000 dm3.

Let’s denote by x the smallest of the dimensions of a given geometric figure.

In the initial data for this task, it is reported that the given dimensions of the rectangular parallelepiped are related to one to two to four, therefore, the average dimension of this geometric figure is 2x dm, and the larger dimension is 4x dm.

According to the condition of the problem, the volume of this geometric figure is one thousand dm³, therefore, we can draw up the following equation:

x * 2x * 4x = 1000,

solving which, we get:

x³ * 8 = 100;

х³ = 1000/8;

x³ = 125;

х³ = 5³;

x = 5 dm.

Therefore, the measurements of this geometric figure are 5 dm, 2 * 5 = 10 dm and 4 * 5 = 20 dm.

Answer: the measurements of this geometric figure are 5 dm, 10 dm and 20 dm.