Question

Может ли существовать треугольник со сторонами 4,6,10? Ответ обоснуйте.

Answer 1

Ответ:

Ответ нет

любая сторона треугольника должна быть меньше чем сумма остальных сторон

10=4+6

не возможно

Answer 2

Ответ:

Нет

Объяснение:

Ведь длина любой стороны треугольника должна быть меньше чем сумма длинн других сторон треугольника

а 4+6=10

Answer 3

Can a triangle with sides 4, 6, and 10 exist?

To determine if a triangle with sides 4, 6, and 10 can exist, we can apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, let's check if the sum of the lengths of the two shorter sides (4 and 6) is greater than the length of the longest side (10):

4 + 6 = 10

The sum of the two shorter sides is equal to the length of the longest side. This means that the triangle inequality is not satisfied, and therefore, a triangle with sides 4, 6, and 10 cannot exist.

In conclusion, a triangle with sides 4, 6, and 10 cannot exist because it violates the triangle inequality theorem.

Answer 4

Can a triangle with sides 4, 6, and 10 exist?

To determine if a triangle with sides 4, 6, and 10 can exist, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this condition is satisfied for the given sides:

- Side 1: 4 - Side 2: 6 - Side 3: 10

The triangle inequality theorem states that:

- Side 1 + Side 2 > Side 3 - Side 2 + Side 3 > Side 1 - Side 1 + Side 3 > Side 2

Let's check these conditions:

- 4 + 6 > 10? Yes, 10 > 10 - 6 + 10 > 4? Yes, 16 > 4 - 4 + 10 > 6? Yes, 14 > 6

All three conditions are satisfied, which means that a triangle with sides 4, 6, and 10 can exist.

Therefore, a triangle with sides 4, 6, and 10 can exist.