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?
□ units
(image shows a line segment 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, \( BC = CD + DB \). So we set up the equation: \( 8x=(3x + 8)+(4x + 10) \)

Step2: Simplify and Solve for \( x \)

Simplify the right - hand side: \( 8x=3x + 8+4x + 10=7x + 18 \)
Subtract \( 7x \) from both sides: \( 8x-7x=7x + 18-7x \), which gives \( x = 18 \)

Step3: Find the Length of \( BC \)

We know that \( BC = 8x \). Substitute \( x = 18 \) into the formula: \( BC=8\times18 = 144 \)

Answer:

144