Question

point d is on segment bc. segment bc measures 8x units in length. what is the length of segment bc? 3x + 8 4x + 10 units

Explanation:

Step1: Apply segment addition postulate

According to the segment addition postulate, \(BC=(3x + 8)+(4x+10)\). Also, it is given that \(BC = 8x\). So, \(3x+8 + 4x+10=8x\).

Step2: Simplify the left - hand side

Combine like terms: \((3x+4x)+(8 + 10)=8x\), which gives \(7x+18 = 8x\).

Step3: Solve for \(x\)

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

Step4: Find the length of \(BC\)

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

Answer:

\(144\)