Question

lies between a and c. if ac = 48, ab = 2x + 2, and bc = 3x + 6, what is bc?

Explanation:

Step1: Use the segment addition postulate

Since \( B \) lies between \( A \) and \( C \), \( AB + BC=AC \). Substitute the given expressions: \( (2x + 2)+(3x + 6)=48 \).

Step2: Simplify the left - hand side of the equation

Combine like terms: \( 2x+3x+2 + 6=48 \), which simplifies to \( 5x+8 = 48 \).

Step3: Solve for \( x \)

Subtract 8 from both sides: \( 5x=48 - 8 \), so \( 5x=40 \). Then divide both sides by 5: \( x=\frac{40}{5}=8 \).

Step4: Find the length of \( BC \)

Substitute \( x = 8 \) into the expression for \( BC \): \( BC=3x + 6 \). So \( BC=3\times8+6=24 + 6=30 \).

Answer:

\( 30 \)