Question

Одна зі сторін паралелограма на 6 см більша за другу. Бісектриса кута паралелограма ділить дiагональ пара- лелограма на вiдрiзки 3 см і 5 см. Знайдіть периметр паралелограма.​

Answer 1

Ответ:

48 см.

Объяснение:

Answer 2

Ответ:

P=2(9+15)=48см

Объяснение:

Ответ:48

Answer 3

To find the perimeter of the parallelogram, we need to determine the lengths of its sides. Let's break down the given information step by step:

1. One side of the parallelogram is 6 cm longer than the other side. 2. The angle bisector of the parallelogram divides one of its diagonals into segments measuring 3 cm and 5 cm.

Let's denote the shorter side of the parallelogram as "x" cm. Therefore, the longer side would be "x + 6" cm.

Finding the Length of the Diagonal

Since the angle bisector divides one of the diagonals into segments measuring 3 cm and 5 cm, we can use the angle bisector theorem to find the length of the diagonal. According to the theorem, the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides of the parallelogram.

Let's denote the length of the diagonal as "d" cm. Using the angle bisector theorem, we can set up the following equation:

3/5 = x/(x + 6)

To solve this equation, we can cross-multiply:

3(x + 6) = 5x

Simplifying the equation:

3x + 18 = 5x

18 = 2x

x = 9

Therefore, the shorter side of the parallelogram is 9 cm, and the longer side is 15 cm (9 + 6).

Calculating the Perimeter

The perimeter of a parallelogram is the sum of all its sides. In this case, since opposite sides of a parallelogram are equal in length, we can calculate the perimeter by adding the lengths of the two shorter sides and multiplying the sum by 2.

Perimeter = 2 * (9 + 15) = 2 * 24 = 48 cm

Therefore, the perimeter of the parallelogram is 48 cm.

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