Applying the segment addition postulate, the length of segment BC is calculated as: 30 units.
What is the Segment Addition Postulate?
Based on the segment addition postulate, when three points A, B and C are collinear (lie on a straight line), where B is at the center of points A and C, thus: AB + BC = AC.
Given the following measurements:
Segment AC = 48,
Segment AB = 2x + 2,
Segment BC = 3x + 6
Plug in the values into AB + BC = AC:
(2x + 2) + (3x + 6) = 48
Solve for x
2x + 2 + 3x + 6 = 48
2x + 3x + 2 + 6 = 48
5x + 8 = 48
Subtract 8 from both sides
5x + 8 - 8 = 48 - 8
5x = 40
Divide both sides by 5
5x/5 = 40/5
x = 8
Find BC by plugging in the value of x
BC = 3(8) + 6
BC = 24 + 6
BC = 30 units.
Therefore, applying the segment addition postulate, the length of segment BC is calculated as: 30 units.
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