Question

В треугольнике АВС проведена биссектриса ВК. Известно, что АВ =6, АК = 3, КС =4 Найдите длину отрезка ВС.

Answer 1

Ответ:

8

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given a triangle ABC with a bisector BK. The lengths of AB, AK, and KC are known to be 6, 3, and 4, respectively. We need to find the length of segment BC.

Solution

To find the length of segment BC, we can use the Angle Bisector Theorem. According to this theorem, in a triangle, the ratio of the lengths of the two segments created by an angle bisector is equal to the ratio of the lengths of the opposite sides.

Let's denote the length of segment BC as x. Using the Angle Bisector Theorem, we can set up the following equation:

AK / KC = AB / BC

Substituting the given values, we have:

3 / 4 = 6 / x

To solve for x, we can cross-multiply and solve the resulting equation:

3x = 4 * 6

Simplifying further:

3x = 24

Dividing both sides by 3:

x = 8

Therefore, the length of segment BC is 8.

Answer

The length of segment BC is 8.