Question

Трёхзвенный шарнир состоит из звеньев длиной 2 см, 5 см и 8 см , которые могут свободно вращаться вокруг точек их соединения . Чему равна разность между наибольшим и наименьшим расстояниями между его концами?

Answer 1

Наименьшее расстояние равно 8 - 5 - 2 = 1 см
Наибольшее равно 8 + 2 + 5 = 15 см.
Разность равна 14 см.

Answer 2

Calculation of the Difference between the Maximum and Minimum Distances

A three-link hinge consists of links with lengths of 2 cm, 5 cm, and 8 cm, which can freely rotate around the points of their connection. We need to find the difference between the maximum and minimum distances between the ends of the hinge.

To calculate this, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the lengths of the links as follows: - Link 1: 2 cm - Link 2: 5 cm - Link 3: 8 cm

To find the maximum distance, we need to arrange the links in a straight line. In this case, the maximum distance will be the sum of the lengths of all the links: - Maximum distance = Link 1 + Link 2 + Link 3 = 2 cm + 5 cm + 8 cm = 15 cm

To find the minimum distance, we need to arrange the links in a triangle. In this case, the minimum distance will be the difference between the sum of the lengths of the two longer links and the length of the shortest link: - Minimum distance = (Link 2 + Link 3) - Link 1 = (5 cm + 8 cm) - 2 cm = 11 cm

Therefore, the difference between the maximum and minimum distances between the ends of the hinge is: - Difference = Maximum distance - Minimum distance = 15 cm - 11 cm = 4 cm

The difference between the maximum and minimum distances between the ends of the three-link hinge is 4 cm.