Question

В треугольнике АВС известно, что АС =32, ВМ- медиана, ВМ =23. найти АМ

Answer 1

32:2=16.
Так как медиана делит основание на 2 равные части.АС-основание

Answer 2

Problem Analysis

We are given a triangle ABC, where AC = 32 and BM is the median with BM = 23. We need to find the length of AM.

Solution

To find the length of AM, we can use the properties of medians in a triangle. The length of a median divides the opposite side into two equal segments. Therefore, we can find the length of AB and BC using the given information and then use the Pythagorean theorem to find the length of AM.

Let's calculate the length of AB and BC first.

From the given information, we know that BM is the median, so it divides the side AC into two equal segments. Therefore, AM = MC.

Using this information, we can calculate the length of AB and BC.

Calculation

Since BM is the median, we have: AM = MC

We also know that AC = 32, so: AM + MC = AC 2 * AM = AC AM = AC / 2

Substituting the value of AC, we get: AM = 32 / 2 AM = 16

Therefore, the length of AM is 16.

Answer

The length of AM is 16.

Explanation

In triangle ABC, the length of AM is equal to the length of MC because BM is the median. Therefore, we can divide the side AC into two equal segments, AM and MC. By using the given length of AC, we can calculate the length of AM as 16.