Question

В треугольнике АВС известно, что АС =54, ВМ - медиана. Найдите АМ.

Answer 1

Медиана делит сторону на две равные части,т.е
AM=MB=1/2AC;
AM=54/2=27

Answer 2

Problem Analysis

We are given a triangle ABC, where AC = 54 and BM is the median. We need to find the length of AM.

Solution

To find the length of AM, we can use the property of medians in a triangle. The median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. It divides the triangle into two equal areas.

Let's denote the midpoint of side AC as D. Since BM is the median, it passes through D. Therefore, BD = DM.

Now, we can use the property of medians to find the length of AM. The length of AM is equal to half the length of BC.

Let's denote the length of BC as x. Then, the length of AM is x/2.

To find the length of BC, we can use the Pythagorean theorem or other geometric properties of the triangle. However, the given information does not provide enough details to determine the length of BC.

Therefore, without additional information, we cannot determine the length of AM.

Conclusion: Without additional information, we cannot determine the length of AM in triangle ABC.