Question

find the value of x and yz if y is between x and z.
xy = 4x, yz = x, and xz = 25

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given values \( XY = 4x \), \( YZ = x \), and \( XZ = 25 \), we get the equation \( 4x + x = 25 \).

Step2: Solve for \( x \)

Combine like terms: \( 5x = 25 \). Then divide both sides by 5: \( x=\frac{25}{5}=5 \).

Step3: Find \( YZ \)

Since \( YZ = x \) and we found \( x = 5 \), then \( YZ = 5 \).

Answer:

\( x = 5 \), \( YZ = 5 \)