In abc, centroid d is on median am. ad = x + 5 and dm = 3x – 5. find am

The length of side AM is

Further explanation:

An altitude is a line that is perpendicular to a side and passes through opposite vertex.

The point at which all the three medians of a triangle intersect each is known as centroid of the triangle.

Median divides the triangle into two equal parts.

Given:

In triangle ABC, D is the centroid on the median AM.

The length of AD is x+5 and the length of DM is 3x-5.

Calculation:

The centroid divides the median in the ratio of

Here, the point D is a median.  

Therefore, D divides the line AM in the ratio of 2:1.

The length of AD is 2 times the length of DM.

The length of side AD can be calculated as follows,

The length of side DM can be calculated as follows,

The length of AM can be calculated as follows,

Hence, the length of side AM is

Learn more:

1. Learn more about inverse of the function link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: perpendicular, altitudes, point, triangle, intersect, centroid, bisectors, perpendicular bisectors, angles,angle bisectors, median, intersection, right angle triangle, equilateral triangle, obtuse, acute.