Question

4.Перпендикуляр, опущений з точки перетину діагоналей ромба на його сторону 8см і ділить цю сторону на відрізки, які відносяться як 2:4. Знайти діагоналі ромба.

Answer 1

Відповідь:

Пояснення:

Answer 2

Finding the Length of the Diagonals of a Rhombus

To find the length of the diagonals of a rhombus when the perpendicular from the point of intersection of the diagonals to one of its sides is 8 cm and divides the side into segments in the ratio 2:4, we can use the properties of a rhombus.

Given: - Perpendicular from the point of intersection of the diagonals to one of its sides = 8 cm - The side is divided into segments in the ratio 2:4

Let's denote the length of the shorter segment as 2x and the length of the longer segment as 4x.

Solution

1. Using the Pythagorean Theorem: - The length of the diagonals can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

2. Calculating the Length of the Diagonals: - Let's consider the diagonals of the rhombus as AC and BD. - The length of the diagonals can be calculated using the formula: - Diagonal 1 (AC) = 2 * √(x^2 + 4x^2) - Diagonal 2 (BD) = 2 * √(2x^2 + 16x^2)

3. Solving for x: - We can solve for x using the given information about the perpendicular and the ratio in which the side is divided.

4. Substituting x to Find the Length of the Diagonals: - Once we find the value of x, we can substitute it into the formulas for the diagonals to find their lengths.

Conclusion

By following these steps, we can determine the lengths of the diagonals of the rhombus based on the given information about the perpendicular and the division of the side into segments.