Question

Поясните, почему не существует треугольника со сторонами, длины которых равны 1см 2мм, 2см 4мм, 3см 6мм.

Answer 1

Потому, что у треугольника должны быть равны 2 (равнобедренный) или 3 (равносторонний) стороны.

Answer 2

Сумма катетов не может быть больше или равна гипотенузе. 

Answer 3

Explanation of the Triangle Problem

The given side lengths of the triangle are 1 cm 2 mm, 2 cm 4 mm, and 3 cm 6 mm. To determine if a triangle can be formed with these side lengths, we can use 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 calculate the sum of the lengths of each pair of sides and compare it to the length of the third side:

1. For the first pair of sides (1 cm 2 mm and 2 cm 4 mm): - Sum of lengths = 1 cm 2 mm + 2 cm 4 mm = 3 cm 6 mm - This sum is equal to the length of the third side (3 cm 6 mm).

2. For the second pair of sides (1 cm 2 mm and 3 cm 6 mm): - Sum of lengths = 1 cm 2 mm + 3 cm 6 mm = 4 cm 8 mm - This sum is greater than the length of the third side (3 cm 6 mm).

3. For the third pair of sides (2 cm 4 mm and 3 cm 6 mm): - Sum of lengths = 2 cm 4 mm + 3 cm 6 mm = 5 cm 10 mm - This sum is greater than the length of the third side (3 cm 6 mm).

Based on the calculations, it is clear that the sum of the lengths of any two sides is greater than the length of the third side for all pairs of sides. Therefore, a triangle can be formed with the given side lengths of 1 cm 2 mm, 2 cm 4 mm, and 3 cm 6 mm.