Question

3 (3 бали), Тупий кут паралелограма дорівние 120°, а висота, що проведена з першини того кута, ділить протилежну сторону на відрізки завдовжки 6 см і 4 см, починаючи з вершини гострого кута. Знайдіть периметр паралело- грама пожалуста я прошу​

Answer 1

Ответ:

44см

Объяснение:

<ABC=120°, по условию

Сумма углов прилежащих к одной стороне параллелограма равна 180° (свойство параллелограма)

<АВС+<ВАD=180° →

<BAD=180°-<ABC=180°-120°=60°

∆ABK- прямоугольный треугольник ВК- высота.

Сумма острых углов в прямоугольном треугольнике равна 90°

<ВАК+<АВК=90°. →

<АВК=90°-<ВАК=90°-60°=30°

АК- катет против угла <АВК=30°

АВ- гипотенуза.

АВ=2*АК=2*6=12 см.

АD=AK+KD=6+4=10см.

Р=2(АВ+АD)=2(12+10)=2*22=44см

Answer 2

Calculation of Perimeter of Parallelogram

To find the perimeter of a parallelogram, we need to know the lengths of its sides. In this case, we are given the lengths of two segments on the opposite side of the parallelogram, which are divided by a height. Let's break down the problem and solve it step by step.

Given information: - The sum of the angles of the obtuse angle of the parallelogram is 120°. - The height divides the opposite side into segments of lengths 6 cm and 4 cm.

To find the perimeter, we need to determine the lengths of the other two sides of the parallelogram.

Finding the Lengths of the Other Two Sides

Since the sum of the angles of the obtuse angle of the parallelogram is 120°, we can conclude that each of the other two angles is 180° - 120° = 60°. This means that the parallelogram is a rhombus, as all angles of a rhombus are equal.

Let's denote the length of one side of the rhombus as x.

Using the properties of a rhombus, we can determine the lengths of the other two sides.

The height of the rhombus divides the opposite side into segments of lengths 6 cm and 4 cm. Since the height is perpendicular to the opposite side, it bisects it. Therefore, the length of the opposite side is 6 cm + 4 cm = 10 cm.

In a rhombus, the diagonals bisect each other at right angles. The height is one of the diagonals, and it bisects the opposite side. Therefore, the length of the other diagonal is also 10 cm.

Using the properties of a rhombus, we can find the lengths of the other two sides.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that the length of each side is equal to half the length of the diagonal.

Therefore, the length of each side of the rhombus is 10 cm / 2 = 5 cm.

Calculation of Perimeter

Now that we know the lengths of all four sides of the parallelogram, we can calculate its perimeter.

The perimeter of a parallelogram is the sum of the lengths of all four sides.

In this case, each side has a length of 5 cm.

Therefore, the perimeter of the parallelogram is 5 cm + 5 cm + 5 cm + 5 cm = 20 cm.

Answer: The perimeter of the parallelogram is 20 cm.