Question

Ученица сказала что если одна сторона треугольника равна 10 см а другая 20 см а третья 30 см то периметр этого треугольника равен 60 см какую ошибку допустила ученица?

Answer 1

Треугольника со сторонами 10,20,30 - не существует :)

Answer 2

Identifying the Error in the Student's Statement

The student made an error in stating that if one side of a triangle is 10 cm, another side is 20 cm, and the third side is 30 cm, then the perimeter of the triangle is 60 cm. However, this statement is incorrect.

The error lies in the understanding of 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 delve into this further.

Triangle Inequality Theorem

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In mathematical terms, for a triangle with sides of lengths a, b, and c, the theorem can be expressed as:

a + b > c a + c > b b + c > a

This means that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Applying the Triangle Inequality Theorem

In the case presented by the student, where one side is 10 cm, another side is 20 cm, and the third side is 30 cm, we can apply the triangle inequality theorem to check if these lengths can form a valid triangle.

Let's verify: - 10 + 20 > 30 (True) - 10 + 30 > 20 (True) - 20 + 30 > 10 (True)

As all the inequalities hold true, the given side lengths can form a valid triangle.

Calculating the Perimeter

Now, let's calculate the perimeter of the triangle with the given side lengths: - Perimeter = 10 + 20 + 30 - Perimeter = 60 cm

Conclusion

The student's error lies in incorrectly stating that the perimeter of the triangle is 60 cm. However, the given side lengths do form a valid triangle, and the perimeter is indeed 60 cm. Therefore, the student's statement is correct in this case.

It's important to understand the principles of the triangle inequality theorem to determine the validity of triangle side lengths and calculate the perimeter accurately.