Question

point c is on line segment \\(overline{bd}\\). given \\(bd = 5x\\), \\(bc = 4x\\), and \\(cd = 4\\), determine the numerical length of \\(overline{bd}\\).

Explanation:

Step1: Use segment addition postulate

Since point \( C \) is on \( \overline{BD} \), we have \( BD = BC + CD \). Substituting the given values, we get \( 5x = 4x + 4 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides of the equation \( 5x = 4x + 4 \): \( 5x - 4x = 4x + 4 - 4x \), which simplifies to \( x = 4 \).

Step3: Find the length of \( \overline{BD} \)

We know \( BD = 5x \), and we found \( x = 4 \). So substitute \( x = 4 \) into \( 5x \): \( BD = 5\times4 = 20 \).

Answer:

\( 20 \)