Mathematics, 30.09.2019 09:30 stophendless9780

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

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Answer from: Fiwui

The length of side AM is $\boxed{12{\text{ units}}}.$

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 $\dfrac{2}{1}.$

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.

$\begin{aligned}{\text{AD}}&= 2\times {\text{DM}}\\x + 5&= 6x - 10\\5 + 10&=6x - x\\15&= 5x\\\frac{{15}}{5}&=x\\3&=x\\\end{aligned}$

The length of side AD can be calculated as follows,

$\begin{aligned}AD&= 3 + 5\\&= 8{\text{ units}}\\\end{aligned}$

The length of side DM can be calculated as follows,

$\begin{aligned}DM &= 3 \times 3 - 5\\&=9 - 5\\&=4\\\end{aligned}$

The length of AM can be calculated as follows,

$\begin{aligned}AM &= AD + DM\\&=8+ 4\\&= 12{\text{ units}}\\\end{aligned}$

Hence, the length of side AM is $\boxed{12{\text{ units}}}.$

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.

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