Question

find the value of x and yz if y is between x and z
xy = 2x + 1, yz = 6x, and xz = 81
x =
yz =

Explanation:

Step1: Use segment addition postulate

Since \(Y\) is between \(X\) and \(Z\), we have \(XY + YZ=XZ\).
Substitute \(XY = 2x + 1\), \(YZ = 6x\), and \(XZ = 81\) into the equation:
\(2x + 1+6x=81\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(8x + 1=81\).

Step3: Solve for \(x\)

Subtract \(1\) from both sides: \(8x=81 - 1=80\).
Divide both sides by \(8\): \(x=\frac{80}{8}=10\).

Step4: Find the value of \(YZ\)

Substitute \(x = 10\) into the formula for \(YZ\). Since \(YZ = 6x\), then \(YZ=6\times10 = 60\).

Answer:

\(x = 10\); \(YZ = 60\)