Question

what is the length of $overline{az}$? use the following information: a is between y and z, ya = 24, az = 15x, and yz = 189.

Explanation:

Step1: Apply segment - addition postulate

Since $A$ is between $Y$ and $Z$, we have $YZ=YA + AZ$.

Step2: Substitute given values

Substitute $YZ = 189$, $YA = 24$, and $AZ=15x$ into the equation: $189=24 + 15x$.

Step3: Solve for $x$

First, subtract 24 from both sides of the equation: $189−24=15x$, so $165 = 15x$. Then divide both sides by 15: $x=\frac{165}{15}=11$.

Step4: Find the length of $AZ$

Since $AZ = 15x$ and $x = 11$, then $AZ=15\times11 = 165$.

Answer:

165