Question

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

Explanation:

Step1: Apply segment - addition postulate

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

Step2: Substitute given values

Substitute $YA = 22$, $AZ = 16x$, and $YZ = 166$ into the equation: $22+16x = 166$.

Step3: Solve for $x$

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

Step4: Find the length of $AZ$

Since $AZ = 16x$ and $x = 9$, then $AZ=16\times9 = 144$.

Answer:

144