Question

В параллелограмме АBCD, АВ=6, АD=8, АС=2корень из 13.Найти BD.

Answer 1

Найдем угол А по теореме косинусов из треугольника АВС:

4*13=36+64-2*6*8cosВ

48=6*8*2cosВ

cosВ=1/2

В=60 градусов

Тогда угол А=(360-2*60)/2=240/2=120.

Запишем теорему косинусов для АВД:

ВД²=36+64+48=148

ВД=4√37

 вроде так=)

Answer 2

Parallelogram ABCD

To find the length of BD in parallelogram ABCD, we can use the properties of a parallelogram. One of the properties states that opposite sides of a parallelogram are equal in length.

Given that AB = 6, AD = 8, and AC = 2√13, we can use this information to find the length of BD.

Solution

Since AB and CD are opposite sides of the parallelogram, they are equal in length. Therefore, CD = AB = 6.

Similarly, AD and BC are opposite sides of the parallelogram, so they are equal in length. Therefore, BC = AD = 8.

Now, let's consider the diagonal AC. According to the properties of a parallelogram, the diagonals of a parallelogram bisect each other. This means that the midpoint of AC is also the midpoint of BD.

Let's find the midpoint of AC:

AC = 2√13

The midpoint of AC is half of AC, so:

Midpoint of AC = (1/2) * AC = (1/2) * 2√13 = √13

Since the midpoint of AC is also the midpoint of BD, we can say that BD is twice the length of the midpoint of AC:

BD = 2 * √13 = 2√13.

Therefore, the length of BD in parallelogram ABCD is 2√13.

Conclusion

In parallelogram ABCD, with AB = 6, AD = 8, and AC = 2√13, the length of BD is 2√13.