Question

applying the segment addition postulate
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 \\(\boldsymbol{\square}\\).
the length of \\(\overline{ab}\\) in inches is \\(\boldsymbol{\square}\\).
the length of \\(\overline{bc}\\) in inches is \\(\boldsymbol{\square}\\).

Explanation:

Step1: Apply Segment Addition Postulate

The Segment Addition Postulate states that if point \( B \) is between \( A \) and \( C \), then \( AB + BC = AC \). Here, \( AB = x \), \( BC = 3x \), and \( AC = 20 \) inches. So we set up the equation:
\( x + 3x = 20 \)

Step2: Solve for \( x \)

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

Step3: Find length of \( \overline{AB} \)

Since \( AB = x \) and \( x = 5 \), the length of \( \overline{AB} \) is 5 inches.

Step4: Find length of \( \overline{BC} \)

Since \( BC = 3x \) and \( x = 5 \), substitute \( x \): \( 3(5) = 15 \) 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 \( 15 \).