Question

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 a) x = 2, bc = 4
o b) x = 2, bc = 8
o c) x = 2, bc = 12
o d) x = 6, bc = 12

Explanation:

Step1: Use segment - addition postulate

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

Step2: Combine like - terms

\(2x+4x=6x\), so the equation becomes \(6x = 12\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 12\) by 6: \(x=\frac{12}{6}=2\).

Step4: Find the value of \(BC\)

Since \(BC = CB\) and \(CB = 2x\), substitute \(x = 2\) into \(CB\). Then \(CB=2\times2 = 4\).

Answer:

A. \(x = 2, BC = 4\)