Question

find the value of a and yz if y is between x and z.
xy = 7a, yz = 5a, xz = 6a + 24

Explanation:

Step1: Use segment addition postulate

Since Y is between X and Z, \( XY + YZ = XZ \). Substitute the given expressions: \( 7a + 5a = 6a + 24 \).

Step2: Simplify and solve for a

Combine like terms: \( 12a = 6a + 24 \). Subtract \( 6a \) from both sides: \( 12a - 6a = 24 \), so \( 6a = 24 \). Divide by 6: \( a = \frac{24}{6} = 4 \).

Step3: Find YZ

Substitute \( a = 4 \) into \( YZ = 5a \): \( YZ = 5 \times 4 = 20 \).

Answer:

\( a = 4 \), \( YZ = 20 \)