Question

1. what are the values of x and bc given the following information?

• b is between c and d;
• cb = 2x;
• bd = 4x, and
• cd = 12.

o x = 2, bc = 4
o x = 2, bc = 8
o x = 2, bc = 12
o x = 6, bc = 12

Explanation:

Step1: Use segment - addition postulate

Since \(B\) is between \(C\) and \(D\), we have \(CB + BD=CD\). Given \(CB = 2x\), \(BD = 4x\), and \(CD = 12\), we substitute these values into the equation: \(2x+4x=12\).

Step2: Combine like - terms

Combining the left - hand side of the equation \(2x + 4x=12\), we get \(6x=12\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(6x = 12\) by 6, we have \(x=\frac{12}{6}=2\).

Step4: Find the length of \(BC\)

Since \(BC = CB\) and \(CB = 2x\), substituting \(x = 2\) into \(CB = 2x\), we get \(CB=2\times2 = 4\).

Answer:

\(x = 2,BC = 4\)