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 144 c 188 d 9

Explanation:

Step1: Use segment - addition postulate

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

Step2: Substitute given values

Substitute \(YA = 22\), \(AZ = 16x\), and \(YZ = 166\) into the equation \(YZ=YA + AZ\), getting \(166=22 + 16x\).

Step3: Solve for \(x\)

First, subtract 22 from both sides of the equation: \(166−22=16x\), so \(144 = 16x\). 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:

B. 144