The length of side AM is [tex]\boxed{7{\text{ units}}}.[/tex]
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+3 and the length of DM is 2x-1.
Calculation:
The centroid divides the median in the ratio of [tex]\dfrac{2}{1}.[/tex]
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.
[tex]\begin{aligned}{\text{AD}}&= 2 \times {\text{DM}}\\x + 3 &= 2 \times\left( {2x - 1} \right)\\x + 3 &= 4x - 2\\3 + 2 &= 4x - x\\5&= 3x\\\frac{5}{3} &= x \\ \end{aligned}[/tex]
The length of side AD can be calculated as follows,
[tex]\begin{aligned}AD&=\Dfrac{5}{3} + 3\\&=\frac{{14}}{3}\\\end{aligned}[/tex]
The length of side DM can be calculated as follows,
[tex]\begin{aligned}DM&= 2\times\frac{5}{3} -1\\&=\frac{{10}}{3} - 1\\&= \frac{{10 - 1}}{3}\\&= \frac{7}{3}\\\end{aligned}[/tex]
The length of AM can be calculated as follows,
[tex]\begin{aligned}AM&= AD + DM\\&= \Dfrac{{14}}{3}+\Dfrac{7}{3}\\&=\Dfrac{{21}}{3}\\&= 7\\\end{aligned}[/tex]
Hence, the length of side AM is [tex]\boxed{7{\text{ units}}}.[/tex]
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
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.
