x = 7XY = 13YZ = 22XZ = 35
Concept:
Here, we need to know the idea of the segment addition postulate.
The segment addition postulate states the given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. In another word, if 3 points A, B, and C are collinear and B is between A and C, then AB + BC = AC.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Given information
XY = x + 6
YZ = 3x + 1
XZ = 5x
Given expression deducted according to the segment addition postulate
XY +YZ = XZ
Substitute values into the expression
x + 6 + 3x + 1 = 5x
Combine like terms
4x + 7 = 5x
Subtract 4x on both sides
4x + 7 - 4x = 5x - 4x
x = 7
Find the value of XY
XY = x + 6 = (7) + 6 = 13
Find the value of YZ
YZ = 3x + 1 = 3 (7) + 1 = 22
Find the value of XZ
XZ = 5x = 5 (7) = 35
Check:
Left-hand side: XY + YZ = 13 + 22 = 35
Right-hand side: XZ = 35
35 = 35
Hope this helps!! :)
Please let me know if you have any questions