Question

ВВ1 – бісектриса трикут­ника АВС. Знайдіть сторону ВС, якщо АВ1:В1С=8:5 і АВ=16 м.

Answer 1

Ответ:

10

Объяснение:

АВ1/В1С=АВ/ВС

8/5=16/х

х=16*5/8 = 10

Answer 2

Bisector of Triangle ABC

To find the length of side BC in triangle ABC, we need to use the given information about the ratio of lengths and the length of side AB.

Let's denote the length of side AB as x. According to the given information, AB1: B1C = 8:5 and AB = 16 m.

To find the length of side BC, we can use the angle bisector theorem. According to this theorem, 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 of the triangle.

In triangle ABC, let AD be the angle bisector of angle BAC, where D lies on side BC. According to the angle bisector theorem, we have:

AB1 / B1C = AB / BC

Substituting the given values, we get:

8/5 = 16 / BC

To find the length of BC, we can cross-multiply and solve for BC:

8 * BC = 5 * 16

BC = (5 * 16) / 8

BC = 10 m

Therefore, the length of side BC in triangle ABC is 10 meters.