Question

find the value of c and yz if y is between x and z. xy = 11, yz = 4c, xz = 83
c =
yz =

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given values \( XY = 11 \), \( YZ = 4c \), and \( XZ = 83 \), we get the equation \( 11 + 4c = 83 \).

Step2: Solve for \( c \)

Subtract 11 from both sides of the equation: \( 4c = 83 - 11 \). Calculating the right side, \( 83 - 11 = 72 \), so \( 4c = 72 \). Then divide both sides by 4: \( c=\frac{72}{4}=18 \).

Step3: Find \( YZ \)

Now that we know \( c = 18 \), substitute \( c \) into the expression for \( YZ \), which is \( 4c \). So \( YZ = 4\times18 = 72 \).

Answer:

\( c = 18 \), \( YZ = 72 \)