Question

point b lies between points a and c on \overline{ac}. let x represent the length of segment ab in inches. use the segment to complete the statements. the value of x is. the length of \overline{ab} in inches is. the length of \overline{bc} in inches is.

Explanation:

Step1: Set up the equation

Since \(AB + BC=AC\), and \(AB = x\), \(BC = 3x\), \(AC = 20\) inches. Then \(x+3x = 20\).

Step2: Solve the equation

Combine like - terms: \(4x=20\). Divide both sides by 4: \(x=\frac{20}{4}=5\).

Step3: Find the length of \(AB\)

Since \(AB=x\), when \(x = 5\), \(AB = 5\) inches.

Step4: Find the length of \(BC\)

Since \(BC = 3x\), substitute \(x = 5\) into \(3x\). Then \(BC=3\times5 = 15\) inches.

Answer:

The value of \(x\) is \(5\).
The length of \(\overline{AB}\) in inches is \(5\).
The length of \(\overline{BC}\) in inches is \(15\).