Question

applying the segment addition postulate
point d is on segment bc. segment bc measures 8x units in length.
what is the length of segment bc?
\boxed{} units
(there is a line segment diagram with points c, d, b. the length from c to d is 3x + 8, and from d to b is 4x + 10)

Explanation:

Step1: Apply Segment Addition Postulate

By the Segment Addition Postulate, \( BC = CD + DB \). Given \( CD = 3x + 8 \), \( DB = 4x + 10 \), and \( BC = 8x \), we substitute these into the equation:
\( 8x=(3x + 8)+(4x + 10) \)

Step2: Simplify and Solve for \( x \)

Combine like terms on the right:
\( 8x = 7x + 18 \)
Subtract \( 7x \) from both sides:
\( x = 18 \)

Step3: Calculate Length of \( BC \)

Substitute \( x = 18 \) into \( BC = 8x \):
\( BC = 8 \times 18 = 144 \)

Answer:

144