Question

1. points b and c are on ad as shown below. the length of ad is 30 units; ac is 16 units long; and bd is 20 units long. how many units long, if it can be determined, is bc? a. 4 b. 6 c. 10 d. 14 e. cannot be determined from the given information

Explanation:

Step1: Use segment - addition postulate

We know that \(AD = 30\), \(AC = 16\), and \(BD=20\). Also, \(AD=AB + BC+CD\), \(AC = AB + BC\), and \(BD=BC + CD\).
Let \(AB=x\), \(BC = y\), and \(CD=z\). So \(x + y+z=30\), \(x + y=16\), \(y + z=20\).

Step2: Solve for \(z\) from \(x + y+z=30\) and \(x + y=16\)

Substitute \(x + y = 16\) into \(x + y+z=30\). We get \(16+z = 30\), then \(z=30 - 16=14\).

Step3: Solve for \(y\) (length of \(BC\))

Since \(y + z=20\) and \(z = 14\), then \(y=20 - 14 = 6\).

Answer:

B. 6