Question

what is the length of $overline{az}$? use the following information: a is between y and z, $ya = 22$, $az = 16x$, and $yz = 166$. a 22 b 188 c 9 d 144

Explanation:

Step1: Apply segment - addition postulate

Since $A$ is between $Y$ and $Z$, we have $YA + AZ=YZ$.
Substitute the given values: $22 + 16x=166$.

Step2: Solve the equation for $x$

Subtract 22 from both sides: $16x=166 - 22$, so $16x = 144$.
Then divide both sides by 16: $x=\frac{144}{16}=9$.

Step3: Find the length of $AZ$

We know $AZ = 16x$. Substitute $x = 9$ into the equation, so $AZ=16\times9 = 144$.

Answer:

D. 144