Question

if bc = 20, cd = x + 11, and bd = 2x + 16, what is bd? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since \(BD=BC + CD\), we have the equation \(2x + 16=20+(x + 11)\).

Step2: Simplify the right - hand side

\(2x + 16=x+31\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(2x - x+16=x - x + 31\), which gives \(x+16 = 31\). Then subtract 16 from both sides: \(x=31 - 16=15\).

Step4: Find \(BD\)

Substitute \(x = 15\) into the expression for \(BD\). \(BD=2x + 16\), so \(BD=2\times15+16\).
\(BD = 30+16=46\).

Answer:

46