Даны пять отрезков,длины которых -различные натуральные числа.Оказалось,что из пяти отрезков можно составить пятиугольник, а вот ни из каких четырех из них четырехугольник составить нельзя.Какое наименьшее значение может принимать длина самого большого отрезка?
The minimum value for the length of the longest segment is 8. This can be proven by constructing a 5-sided polygon with the given segments, which satisfies the requirement of being a pentagon. In addition, by assuming a smaller value for the longest segment, it can be proven that it is not possible to construct a 5-sided polygon. In order to construct the pentagon, the angles of the polygon must satisfy the triangle inequality, which states that the sum of the lengths of any two sides must be greater than the length of the third side. By drawing diagrams and doing some algebraic manipulations, it can be shown that the smallest possible value for the longest segment is 8. This is because the sum of the two shortest segments must be greater than the sum of the two longer segments in order to satisfy the triangle inequality. Therefore, all five segments must have lengths 1, 2, 3, 4, and 5 respectively, and by rearranging these segments, a 5-sided polygon can be constructed. This is the minimum value for the length of the longest segment, and any value smaller than 8 will not fulfill the requirements of the problem.
