Applying the definition of the median of a triangle: x = 9; CD = 28; DB = 28.
What is the Median of a Triangle?
The median of a triangle can be defined as a line segment in a triangle that joins the vertex of a triangle to the midpoint of the side of the triangle that is opposite the vertex.
Given triangle ABC, where AD is the median and D is the midpoint of side AB, therefore:
Side CD equals side DB.
Side CD = 5x - 17
Side DB = 3x + 1
Make both segments equal to each other. Therefore, we would have the equation:
5x - 17 = 3x + 1
Solve for x
Add both sides by 17
5x - 17 + 17 = 3x + 1 + 17
5x = 3x + 18
Subtract 3x from both sides
5x - 3x = 3x + 18 - 3x
2x = 18
Divide both sides by 2
2x/2 = 18/2
x = 9
CD = 5x - 17
Plug in the value of x
CD = 5(9) - 17
CD = 45 - 17
CD = 28 units.
DB = 3x + 1
Plug in the value of x
DB = 3(9) + 1
DB = 27 + 1
DB = 28 units.
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