Question

find the value of n and yz if y is between x and z. xy = 5n, yz = 2n, xz = 91

Explanation:

Step1: Use segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given values, we get \( 5n + 2n = 91 \).

Step2: Solve for \( n \)

Combine like terms: \( 7n = 91 \). Then divide both sides by 7: \( n=\frac{91}{7}=13 \).

Step3: Find \( YZ \)

Substitute \( n = 13 \) into \( YZ = 2n \), so \( YZ = 2\times13 = 26 \).

Answer:

\( n = 13 \), \( YZ = 26 \)