Question

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

Explanation:

Step1: Set up the equation

Since \(BC = CD + DB\), we have \(8x=(3x + 8)+(4x + 10)\).

Step2: Simplify the right - hand side

Combine like terms: \((3x+4x)+(8 + 10)=7x+18\). So the equation becomes \(8x=7x + 18\).

Step3: Solve for \(x\)

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

Step4: Find the length of \(BC\)

Substitute \(x = 18\) into \(BC = 8x\). Then \(BC=8\times18\).

Answer:

\(144\)