Answer:
The value of x is 5
The length of YZ is 5 units
Step-by-step explanation:
If a point lies on a line segment, then it divides it into 2 parts, the sum of their length equals the length of the line segment
Let us use this fact to solve the question
∵ Point Y is between points X and Z
→ By using the fact above
∴ XY + YZ = XZ
∵ XY = 4x and XZ = x
∵ XZ = 25
→ Substitute then in the equation above
∴ 4x + x = 25
→ Add the like terms in the left side
∴ 5x = 25
→ Divide both sides by 5 to find x
∵ [tex]\frac{5x}{5}[/tex] = [tex]\frac{25}{5}[/tex]
∴ x = 5
∴ The value of x is 5
∵ YZ = x
∵ x = 5
∴ YZ = 5
∴ The length of YZ is 5 units
