Question

c is the midpoint of \\( \overline { b d } \\). if \\( b c = 5 x \\) and \\( c d = x + 8 \\), what is \\( b c \\)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the midpoint property

Since \(C\) is the midpoint of \(\overline{BD}\), \(BC = CD\). So, \(5x=x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(5x-x=x + 8-x\), which gives \(4x=8\). Then divide both sides by \(4\): \(x=\frac{8}{4}=2\).

Step3: Find the value of \(BC\)

Substitute \(x = 2\) into \(BC = 5x\). So, \(BC=5\times2 = 10\).

Answer:

\(10\)