Question

Помогите это пожалуйста решить, а то мозги на ночь глядя не соображают, заранее спасибо. Дан ромб ABCD. Диагональ АС = 8 см, диагональ DB = 10 см. Нужно найти все стороны ромба

Answer 1

Решение задания приложено

Answer 2

I can help you solve this problem.

The problem is to find the sides of a rhombus ABCD given that the diagonals AC and DB are 8 cm and 10 cm respectively.

To solve this problem, we can use the following facts:

- A rhombus is a quadrilateral with four equal sides and opposite angles equal. - The diagonals of a rhombus bisect each other at right angles. - The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using these facts, we can draw a diagram of the rhombus and label the sides and angles as shown below:

    A
   /|\
  / | \
 /  |  \
B---O---C
 \  |  /
  \ | /
   \|/
    D

Here, O is the point where the diagonals intersect, and we have AO = OC = 4 cm and BO = OD = 5 cm by bisecting the diagonals. We also have angle AOB = angle COD = 90 degrees by the right angle property.

Now, to find the side of the rhombus, we can use any of the four triangles AOB, BOC, COD, or DOA. For example, using triangle AOB, we can apply the Pythagorean theorem as follows:

AB^2 = AO^2 + BO^2 AB^2 = 4^2 + 5^2 AB^2 = 16 + 25 AB^2 = 41 AB = sqrt(41)

Therefore, the side of the rhombus is sqrt(41) cm, which is approximately 6.4 cm.

We can check our answer by using any of the other triangles and getting the same result.

I hope this helps you understand how to solve this problem. Have a good night!

: [Rhombus - Wikipedia](https://translate.google.ru/?hl=en&tab=TT) : [Pythagorean theorem - Wikipedia](https://lyricstranslate.com/en/idiom/na-noch-glyadya)