Question

Точка В відрізка АС ділить його на дві частини, які відносяться як 1:4. Знайдіть відрізки АВ і ВС, якщо АС = 40 см. Помогите!

Answer 1

Объяснение:

АВ=х см

ВС=4х см

АС=40 см

АВ+ВС=АС

х+4х=40

5х=40

х=8

АВ=8 см

ВС=4×8=32 см

Answer 2

Problem Analysis

We are given that a line segment AC is divided into two parts, with the ratio of their lengths being 1:4. We need to find the lengths of segments AB and BC, given that AC is 40 cm.

Solution

Let's assume that the length of segment AB is x cm. Since the ratio of AB to BC is 1:4, the length of segment BC would be 4x cm.

According to the problem, the sum of the lengths of AB and BC is equal to the length of AC. Therefore, we can write the following equation:

x + 4x = 40

Simplifying the equation, we get:

5x = 40

Dividing both sides of the equation by 5, we find:

x = 8

Now that we have the value of x, we can find the lengths of AB and BC:

AB = x = 8 cm BC = 4x = 4 * 8 = 32 cm

Therefore, the lengths of AB and BC are 8 cm and 32 cm, respectively.

Answer

The length of segment AB is 8 cm and the length of segment BC is 32 cm.