Question

Сторони паралелограма дорівнюють 23 см і 11 см. Знайдіть діагоналі паралелограма, якщо вони відносяться як 2 : 3. Пожалуйста решите,очень надо.За нее спасибо.

Answer 1

У параллелограмма есть полезное свойство:
Сумма квадратов диагоналей равна сумме квадратов всех его сторон. 
Пусть коэффициент отношения диагоналей будет х.
Тогда d=2x , D=3x
2*23²+2*11²=4х³+9х²
13х²=1300
х²=100
х=10
d=10*2=20 см
D=10*3=30 см

Answer 2

Finding the Diagonals of a Parallelogram

To find the diagonals of a parallelogram, we need to use the given information about the sides and the ratio of the diagonals. Let's break down the problem step by step.

Given: - The sides of the parallelogram are 23 cm and 11 cm. - The ratio of the diagonals is 2:3.

To find the length of the diagonals, we can use the following formula:

Diagonal 1 = (Side 1) * √(4x² - 1) / 3 Diagonal 2 = (Side 2) * √(4x² - 1) / 3

Here, x represents the ratio of the diagonals, which is 2:3 in this case.

Let's substitute the given values into the formula:

Diagonal 1 = (23 cm) * √(4(2/3)² - 1) / 3 Diagonal 2 = (11 cm) * √(4(2/3)² - 1) / 3

Now, let's calculate the diagonals using the formula:

Diagonal 1 = (23 cm) * √(4(2/3)² - 1) / 3 Diagonal 2 = (11 cm) * √(4(2/3)² - 1) / 3

Calculating the values:

Diagonal 1 = (23 cm) * √(4(4/9) - 1) / 3 Diagonal 2 = (11 cm) * √(4(4/9) - 1) / 3

Diagonal 1 = (23 cm) * √(16/9 - 1) / 3 Diagonal 2 = (11 cm) * √(16/9 - 1) / 3

Diagonal 1 = (23 cm) * √(16/9 - 9/9) / 3 Diagonal 2 = (11 cm) * √(16/9 - 9/9) / 3

Diagonal 1 = (23 cm) * √(7/9) / 3 Diagonal 2 = (11 cm) * √(7/9) / 3

Now, let's simplify the square root:

Diagonal 1 = (23 cm) * √(7/9) / 3 Diagonal 2 = (11 cm) * √(7/9) / 3

Diagonal 1 = (23 cm) * (√7 / √9) / 3 Diagonal 2 = (11 cm) * (√7 / √9) / 3

Diagonal 1 = (23 cm) * (√7 / 3) / 3 Diagonal 2 = (11 cm) * (√7 / 3) / 3

Finally, let's calculate the diagonals:

Diagonal 1 ≈ (23 cm) * (0.745 / 3) ≈ 5.68 cm Diagonal 2 ≈ (11 cm) * (0.745 / 3) ≈ 2.68 cm

Therefore, the approximate lengths of the diagonals of the parallelogram are 5.68 cm and 2.68 cm.

Please note that the above calculations are based on the given information and the formula for finding the diagonals of a parallelogram.