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

Explanation:

Step1: Apply Segment Addition Postulate

By the Segment Addition Postulate, \( BC = CD + DB \). So we have the equation \( 8x=(3x + 8)+(4x + 10) \).

Step2: Simplify the right - hand side

Simplify the right - hand side of the equation: \( (3x + 8)+(4x + 10)=3x+4x + 8 + 10=7x+18 \). So the equation becomes \( 8x=7x + 18 \).

Step3: Solve for x

Subtract \( 7x \) from both sides of the equation \( 8x=7x + 18 \): \( 8x-7x=7x + 18-7x \), which gives \( x = 18 \).

Step4: Find the length of BC

Since \( BC = 8x \) and \( x = 18 \), then \( BC=8\times18 = 144 \).

Answer:

144