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

According to the Segment Addition Postulate, \(BC = CD+DB\). Given \(BC = 8x\), \(CD=3x + 8\), and \(DB = 4x+10\). So, \(8x=(3x + 8)+(4x + 10)\).

Step2: Simplify the equation

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

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(8x-7x=7x + 18-7x\). So, \(x = 18\).

Step4: Find the length of \(BC\)

Since \(BC = 8x\), substitute \(x = 18\) into the formula. Then \(BC=8\times18\).

Answer:

\(144\)