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 5
the length of \\(\overline{ab}\\) in inches is 15
the length of \\(\overline{bc}\\) in inches is
options: 4, 5, 15, 20

Explanation:

Step1: Recall the Segment Addition Postulate

The Segment Addition Postulate states that if point \( B \) is between points \( A \) and \( C \), then \( AB + BC = AC \). From the diagram, \( AB = x \), \( BC = 3x \), and \( AC = 20 \) inches. So we have 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 the length of \( BC \)

Since \( BC = 3x \) and \( x = 5 \), substitute \( x \) into the expression for \( BC \): \( BC = 3\times5 = 15 \) inches.

Answer:

The length of \( \overline{BC} \) in inches is \( 15 \).