Question

Серединный перпендикуляр к стороне AB треугольника ABC пересекает сторону BC в точке E. Найдите AC, если BC=24 см, а периметр треугольника AEC равен 30см. Желательно с картинкой.

Answer 1

треугольник АВС, ЕН-серединный перпендикуляр на АВ, АН=ВН, ВС=24=ВЕ+ЕС, периметрАЕС=30=АЕ+ЕС+АС, треугольник АВН, ЕН-высота=медиана, только в равнобедренном треугольнике высота проведенная к основанию=медиане, АЕ=ВЕ, перметрАЕС=АЕ(ВЕ)+ЕС+АС, 30=ВЕ+ЕС+АС, 30=24+АС, АС=6

Answer 2

Problem Analysis

We are given a triangle ABC, where the midpoint of side AB is connected to point E on side BC. We are also given that the perimeter of triangle AEC is 30 cm and that BC is 24 cm. We need to find the length of side AC.

Solution

To solve this problem, we can use the concept of similar triangles. Let's denote the length of AC as x.

Since the midpoint of side AB is connected to point E, we can conclude that AE is equal to BE. Therefore, the length of AE is 12 cm (half of BC).

Now, let's consider triangle ABC and triangle AEC. These two triangles share the same angle at point A. By the Angle-Angle (AA) similarity criterion, we can conclude that these two triangles are similar.

Using the similarity of triangles ABC and AEC, we can set up the following proportion:

AC / AE = BC / EC

Substituting the given values, we have:

x / 12 = 24 / EC

To find EC, we can subtract AE from BC:

EC = BC - AE = 24 - 12 = 12 cm

Substituting this value into the proportion, we have:

x / 12 = 24 / 12

Simplifying the equation, we get:

x = 24

Therefore, the length of side AC is 24 cm.

Diagram

Here is a diagram to help visualize the problem:

       A
      / \
     /   \
    /     \
   /       \
  /         \
 B-----------C
      E

In this diagram, AB = BC = 24 cm, AE = 12 cm, and AC = 24 cm.

I hope this helps! Let me know if you have any further questions.