Question

На отрезке АВ длинной 36 см взята точка К .Найти длину отрезков АК и ВК , если АК:ВК=4:5 . СРОЧНО!!ПОМОГИТЕЕ!

Answer 1

1 часть = 36/9=4
АК=4•4=16
ВК=5•4=20

Answer 2

Problem Statement

You have a line segment AB with a length of 36 cm, and a point K is taken on this line segment. You need to find the lengths of the line segments AK and BK, given that the ratio of AK to BK is 4:5.

Solution

To solve this problem, we can use the concept of dividing a line segment in a given ratio. The formula for dividing a line segment in a given ratio is:

The formula for dividing a line segment in a given ratio: If a line segment AB is divided by a point K such that AK:KB = m:n, then the coordinates of the point K are given by: \[ K(x, y) = \left( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \right) \]

Where: - \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points A and B, respectively. - m and n are the parts into which the line segment is divided.

Calculation

Given: - Length of line segment AB = 36 cm - Ratio of AK to BK = 4:5

Using the formula, we can calculate the lengths of AK and BK.

Let's calculate the lengths of AK and BK using the given ratio and the length of line segment AB.

Length of AK and BK

Using the given ratio of AK to BK (4:5) and the length of line segment AB (36 cm), we can calculate the lengths of AK and BK as follows:

\[ AK = \frac{4}{4+5} \times 36 \] \[ BK = \frac{5}{4+5} \times 36 \]

Result

After calculating the above expressions, we find: - Length of AK = 16.8 cm - Length of BK = 19.2 cm

Therefore, the lengths of the line segments AK and BK are 16.8 cm and 19.2 cm, respectively.

I hope this helps! If you have any further questions, feel free to ask.