Question

Диагонали паралелограмма = 34 и 38 см. , а стороны относятся как 2:3. Найти периметр паралелограмма.

Answer 1

Из отношения сторон 2:3 ясно, что одна сторона составляет 2 части, другая 3.
Пусть а - одна часть, тогда
2а - меньшая сторона
3а - большая сторона.
У паралелограмма есть зависимость между его сторонами и диагоналями.
Сумма квадратов диагоналей равна сумме квадратов его сторон.
((2а)^2 + (3a)^2) * 2 = 34^2 + 38^2
(4a^2 + 9a^2) * 2 = 2600
4a^2 + 9a^2 = 1300
13a^2 = 1300
a^2 = 100
a = 10
Тогда:
10 * 2 = 20 (см) - меньшая сторона
10 * 3 = 30 (см) - большая сторона
Р = (20 + 30) * 2 =100 (см)
Ответ: 100 см

Answer 2

Given Information:

We are given that the diagonals of a parallelogram are 34 cm and 38 cm, and the sides are in the ratio of 2:3. We need to find the perimeter of the parallelogram.

Solution:

To find the perimeter of the parallelogram, we need to determine the lengths of all four sides.

Let's assume the lengths of the sides are 2x and 3x, where x is a common factor.

From the given information, we know that the diagonals of a parallelogram bisect each other. Therefore, we can use the properties of a parallelogram to find the lengths of the sides.

Using the property that the diagonals of a parallelogram bisect each other, we can form two right triangles. The diagonals of the parallelogram act as the hypotenuses of these right triangles.

Let's consider one of the right triangles formed by the diagonals. The lengths of the sides of this right triangle are:

- One leg: half the length of one diagonal = 34/2 = 17 cm - The other leg: half the length of the other diagonal = 38/2 = 19 cm

Using the Pythagorean theorem, we can find the length of the third side (the base of the right triangle):

c^2 = a^2 + b^2

c^2 = 17^2 + 19^2

c^2 = 289 + 361

c^2 = 650

c ≈ 25.5 cm

Now, we can find the lengths of the sides of the parallelogram:

- One side: 2x = 2 * 17 = 34 cm - The adjacent side: 3x = 3 * 19 = 57 cm

To find the perimeter, we add up the lengths of all four sides:

Perimeter = 34 + 57 + 34 + 57 = 182 cm

Therefore, the perimeter of the parallelogram is 182 cm.

Summary:

The perimeter of the parallelogram with diagonals measuring 34 cm and 38 cm, and sides in the ratio of 2:3, is 182 cm.