Question

В треугольнеке ABC прямая MN,параллейная стороне AC ,делит сторону BC на отрезки BN=15см. и NC=5 см. ,а сторону AB на BM и AM. Найдите длину отрезка MN если AC=15см. Пришлите решение пажалуйста.

Answer 1

1) Прямая MN, паралельная стороне треугольника AC, отсекает треугольник MBN, подобный треугольнику ABC.
2) AC/MN=BC/BN (BC = 15 + 5 = 20 см)
   MN = AC×BN÷BC
   MN = 15×15÷20 = 11.25 см

Answer 2

Problem Analysis

We are given a triangle ABC with a line MN parallel to side AC. The line MN divides side BC into segments BN and NC, and side AB into segments BM and AM. We need to find the length of segment MN when AC = 15 cm.

Solution

To find the length of segment MN, we can use the concept of similar triangles. Let's analyze the given information and use it to find the length of MN.

From the given information, we have: - BN = 15 cm - NC = 5 cm - AC = 15 cm

Let's denote the length of segment BM as x and the length of segment AM as y.

Using the concept of similar triangles, we can set up the following ratios:

1. Ratio of lengths of corresponding sides in triangles ABM and ACN: BM/AC = AM/NC 2. Ratio of lengths of corresponding sides in triangles ABN and ACN: BN/AC = AM/NC From equation (1), we can rewrite it as: BM = (AC * AM) / NC From equation (2), we can rewrite it as: BN = (AC * AM) / NC Since BN = 15 cm and NC = 5 cm, we can substitute these values into equation (2) to solve for AM: 15 = (AC * AM) / 5 AM = (15 * 5) / AC

Now, we can substitute the value of AM into equation (1) to solve for BM: BM = (AC * AM) / NC BM = (AC * (15 * 5) / AC) / 5 BM = 15

Therefore, the length of segment BM is 15 cm.

To find the length of segment MN, we can add the lengths of BN and NC: MN = BN + NC MN = 15 + 5 MN = 20

Therefore, the length of segment MN is 20 cm.

Answer

The length of segment MN is 20 cm.

Please let me know if you need any further clarification.