Question

Точки Д,С,Е лежат на отрезке АВ. Точка Д середина отрезка АС, а точка Е середина отрезка СВ. Расстояние между точками Д и Е равно 16 см. Найдите длину отрезка АВ. Как записать решение?

Answer 1

16-18=22    от точки д к точки а

Answer 2

Problem Analysis

We are given that points D, C, and E lie on the line segment AB. Point D is the midpoint of segment AC, and point E is the midpoint of segment CV. The distance between points D and E is 16 cm. We need to find the length of segment AB.

Solution

To find the length of segment AB, we can use the fact that D is the midpoint of segment AC and E is the midpoint of segment CV. This means that the lengths of segments AD and DC are equal, and the lengths of segments CE and EV are also equal.

Let's denote the length of segment AD as x. Since D is the midpoint of segment AC, the length of segment DC is also x. Similarly, since E is the midpoint of segment CV, the length of segment CE is also x.

Now, we can express the length of segment AB in terms of x. Segment AB can be divided into three parts: segment AD, segment DC, and segment CV. So, the length of segment AB is equal to the sum of the lengths of these three segments:

AB = AD + DC + CV

Since AD = DC = x and CE = x, we can substitute these values into the equation:

AB = x + x + x

Simplifying the equation, we get:

AB = 3x

We are given that the distance between points D and E is 16 cm. Since D is the midpoint of segment AC and E is the midpoint of segment CV, the length of segment DE is half the length of segment AC or CV. So, we have:

DE = 16/2 = 8 cm

We can express the length of segment DE in terms of x as well. Segment DE can be divided into two parts: segment DC and segment CE. So, the length of segment DE is equal to the sum of the lengths of these two segments:

DE = DC + CE

Since DC = CE = x, we can substitute these values into the equation:

DE = x + x

Simplifying the equation, we get:

DE = 2x

We are given that DE = 16 cm, so we can set up the following equation:

2x = 16

Solving for x, we find:

x = 16/2 = 8 cm

Now that we know the value of x, we can find the length of segment AB:

AB = 3x = 3 * 8 = 24 cm

Therefore, the length of segment AB is 24 cm.

Answer

The length of segment AB is 24 cm.

Explanation

We can solve this problem by using the fact that D is the midpoint of segment AC and E is the midpoint of segment CV. By setting up equations based on this information, we can find the length of segment AB. Let's denote the length of segment AD as x. Since D is the midpoint of segment AC, the length of segment DC is also x. Similarly, since E is the midpoint of segment CV, the length of segment CE is also x. We can express the length of segment AB in terms of x as AB = AD + DC + CV. Simplifying the equation, we get AB = 3x. We are given that the distance between points D and E is 16 cm, which is equal to the length of segment DE. Since DE = DC + CE, we can substitute the values of DC and CE as x into the equation. Simplifying the equation, we get 2x = 16. Solving for x, we find x = 8 cm. Finally, we can find the length of segment AB by substituting the value of x into the equation AB = 3x. Therefore, the length of segment AB is 24 cm.