Question

Сумма диагоналей параллелограмма равна 22 см а его стороны равны 7 см и 9 см найти диагонали параллелограмма

Answer 1

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Answer 2

Finding the Diagonals of a Parallelogram

To find the diagonals of a parallelogram, we need to use the given information about the sum of the diagonals and the lengths of the sides.

Given: - The sum of the diagonals of the parallelogram is 22 cm. - The sides of the parallelogram are 7 cm and 9 cm.

Let's denote the diagonals as d1 and d2.

To find the diagonals, we can use the following formulas:

d1^2 = a^2 + b^2 + 2ab * cos(θ) d2^2 = a^2 + b^2 - 2ab * cos(θ)

Where: - a and b are the lengths of the sides of the parallelogram. - θ is the angle between the sides of the parallelogram.

In a parallelogram, opposite sides are equal in length, and opposite angles are congruent. Therefore, we can assume that the angle between the sides is 180 degrees.

Using the given lengths of the sides (7 cm and 9 cm), we can substitute these values into the formulas:

d1^2 = 7^2 + 9^2 + 2 * 7 * 9 * cos(180) d2^2 = 7^2 + 9^2 - 2 * 7 * 9 * cos(180)

Simplifying the equations:

d1^2 = 49 + 81 + 2 * 7 * 9 * (-1) d2^2 = 49 + 81 - 2 * 7 * 9 * (-1)

d1^2 = 49 + 81 - 126 d2^2 = 49 + 81 + 126

d1^2 = 4 d2^2 = 256

Taking the square root of both sides to find the diagonals:

d1 = 2 cm d2 = 16 cm

Therefore, the diagonals of the parallelogram are 2 cm and 16 cm.