Question

find the value of x and yz if y is between x and z. 5. xy = 4x, yz = 3x, and xz = 42

Explanation:

Step1: Use segment - addition postulate

Since $Y$ is between $X$ and $Z$, we have $XY + YZ=XZ$. Given $XY = 4x$, $YZ = 3x$, and $XZ = 42$, we substitute these values into the equation: $4x+3x = 42$.

Step2: Combine like - terms

Combining the left - hand side of the equation $4x+3x = 42$, we get $7x=42$.

Step3: Solve for $x$

Divide both sides of the equation $7x = 42$ by 7. So, $x=\frac{42}{7}=6$.

Step4: Find the value of $YZ$

Since $YZ = 3x$ and $x = 6$, then $YZ=3\times6 = 18$.

Answer:

$x = 6$, $YZ = 18$