Question

Отрезок KL пересекает плоскость β в точке O, без него на плоскости находятся ещё две точки M и N так, что MK параллельна NL. MK = 5 дм, LN = 15 дм, KL = 24 дм.Вычислите KO и OL. Воссоздайте данный рисунок и объясните ход решения.

Answer 1

Треугольники подобны по 3 углам
с к=15/5=3
Значит LO/Ok=3
KO=24/4=6
OL=24-6=18

Answer 2

Problem Statement

We are given a line segment KL that intersects a plane β at point O. Additionally, there are two other points M and N on the plane such that MK is parallel to NL. The lengths of MK, LN, and KL are given as 5 dm, 15 dm, and 24 dm, respectively. We need to calculate the lengths of KO and OL.

Solution

To solve this problem, we can use the concept of similar triangles. Let's analyze the given information and construct a diagram to better understand the problem.

1. We have a line segment KL that intersects the plane β at point O. 2. There are two other points, M and N, on the plane β such that MK is parallel to NL. 3. The lengths of MK, LN, and KL are given as 5 dm, 15 dm, and 24 dm, respectively.

Let's construct the diagram:

      K-----------------L
      |                 |
      |                 |
      |                 |
      |        O        |
      |                 |
      |                 |
      M-----------------N

Now, let's analyze the diagram and the given information:

1. We have a line segment KL that intersects the plane β at point O. 2. MK is parallel to NL. 3. MK = 5 dm, LN = 15 dm, KL = 24 dm.

From the given information, we can observe that triangles KOM and LON are similar because MK is parallel to NL. This means that the corresponding sides of these triangles are proportional.

Let's set up the proportion:

MK / KO = LN / LO

Substituting the given values:

5 dm / KO = 15 dm / LO

Cross-multiplying:

5 dm * LO = 15 dm * KO

Simplifying:

LO = (15 dm * KO) / 5 dm

LO = 3 * KO

We also know that KL = KO + LO. Substituting the value of LO:

24 dm = KO + 3 * KO

24 dm = 4 * KO

Simplifying:

KO = 24 dm / 4

KO = 6 dm

Now, we can calculate the value of LO:

LO = 3 * KO

LO = 3 * 6 dm

LO = 18 dm

Therefore, the lengths of KO and OL are 6 dm and 18 dm, respectively.

Conclusion

In this problem, we were given a line segment KL that intersects a plane β at point O. We also had two other points, M and N, on the plane such that MK is parallel to NL. By using the concept of similar triangles, we were able to calculate the lengths of KO and OL as 6 dm and 18 dm, respectively.