Question

В параллелограмме АВСD AE-биссектриса угла А. Стороны параллелограмма АВ и ВС Относятся 4:9 АЕ Пересекает диагональ BD в точке К. Найдите отношение BK:KD. С решением, пожалуйстааа

Answer 1

Там скорее всего идет речь про подобие треугольников. BK:KD=4:9

Answer 2

Given Information:

We are given the following information about the parallelogram ABCD: - AE is the angle bisector of angle A. - The sides AB and BC are in a ratio of 4:9. - AE intersects the diagonal BD at point K.

Solution:

To find the ratio BK:KD, we need to determine the lengths of BK and KD.

Let's start by finding the lengths of AB and BC. Since AB and BC are in a ratio of 4:9, we can assign a variable to one of the lengths and express the other length in terms of that variable.

Let's assume the length of AB is 4x. Therefore, the length of BC would be 9x.

Now, let's consider triangle ABE. Since AE is the angle bisector of angle A, we can use the angle bisector theorem to find the ratio of the lengths of BE and EA.

According to the angle bisector theorem, the ratio of the lengths of BE and EA is equal to the ratio of the lengths of BC and AC.

Since BC is 9x and AC is 4x (as AB and BC are in a ratio of 4:9), the ratio of BE to EA is 9x:4x, which simplifies to 9:4.

Now, let's consider triangle BDK. Since AE is the angle bisector of angle A, we can use the angle bisector theorem again to find the ratio of the lengths of BK and KD.

According to the angle bisector theorem, the ratio of the lengths of BK and KD is equal to the ratio of the lengths of BE and ED.

Since BE is 9x and ED is 4x (as BE and EA are in a ratio of 9:4), the ratio of BK to KD is 9x:4x, which simplifies to 9:4.

Therefore, the ratio BK:KD is 9:4.

Please let me know if you need any further clarification or assistance.