Question

find the value of x and yz if y is between x and z. xy = 12, yz = 2x, and xz = 28

Explanation:

Step1: Use segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given values: \( 12 + 2x = 28 \).

Step2: Solve for \( x \)

Subtract 12 from both sides: \( 2x = 28 - 12 = 16 \). Then divide by 2: \( x = \frac{16}{2} = 8 \).

Step3: Find \( YZ \)

Substitute \( x = 8 \) into \( YZ = 2x \): \( YZ = 2\times8 = 16 \).

Answer:

\( x = 8 \); \( YZ = 16 \)