Question

Какое из следующих утверждений верно ? 1 ) площадь любого параллелограма равна произведению длин его сторон 2 ) треугольник со сторонами 1,2,4 существует 3) у любой трапеции основания параллельны

Answer 1

3 утверждение правильно

Answer 2

Statement 1: The area of any parallelogram is equal to the product of its side lengths.

This statement is true. The area of a parallelogram is indeed equal to the product of the lengths of its adjacent sides multiplied by the sine of the angle between them. Mathematically, it can be expressed as:

Area = base * height = |a| * |b| * sin(θ)

Where |a| and |b| are the lengths of the adjacent sides, and θ is the angle between them.

Statement 2: A triangle with side lengths 1, 2, and 4 exists.

This statement is false. According to the triangle inequality 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, 1 + 2 = 3, which is less than 4. Therefore, a triangle with side lengths 1, 2, and 4 does not exist.

Statement 3: In any trapezoid, the bases are parallel.

This statement is true. In a trapezoid, the bases are two parallel sides. The other two sides, called the legs, are not parallel. The bases of a trapezoid are the only sides that are parallel to each other.

To summarize: 1. The area of any parallelogram is equal to the product of the lengths of its adjacent sides. 2. A triangle with side lengths 1, 2, and 4 does not exist. 3. In any trapezoid, the bases are parallel