Question

6. На прямой отложены два равных отрезка АС и Св. На отрезке CB взята точка D, которая делит его в отношении 3:1, считая от точки с. Найдите расстояние между А и В, если CD=9 см. [5]​

Answer 1

Объяснение:

9

×—————-×———×—×

А С D B

3x x

CD=9 cм

DB=x

CD=3x

3x=9

X=3

DB=3 см

CB=CD+DB=9+3=12 см

AC=CB=12 см

AB=2×AC=2×12=24 см

Answer 2

Problem Analysis

We are given a line segment AB, where AB is equal to AC and CV. Point D is taken on the line segment CB, dividing it in the ratio 3:1, counting from point C. We need to find the distance between points A and B, given that CD is 9 cm.

Solution

Let's denote the distance between points A and B as x. Since CD divides CB in the ratio 3:1, we can write the following equation:

AC/CD = 3/1

Since AC is equal to AB, we can substitute AB for AC:

AB/CD = 3/1

Now we can substitute the given value of CD as 9 cm:

AB/9 = 3/1

To find AB, we can cross-multiply and solve for AB:

AB = (3/1) * 9

AB = 27 cm

Therefore, the distance between points A and B is 27 cm.

Answer

The distance between points A and B is 27 cm.