Question

in the figure above, ab : bc is 3 : 1 and ac = 48. the length of ab is:
4.
12.
36.
none of these choices are correct.

Explanation:

Step1: Define the ratio parts

Let the length of \( AB = 3x \) and \( BC = x \) (since \( AB:BC = 3:1 \)).

Step2: Relate to total length \( AC \)

We know that \( AC = AB + BC \) (from the segment addition postulate). Substituting the values, we get \( 3x + x = 48 \).

Step3: Solve for \( x \)

Simplify the left - hand side: \( 4x = 48 \). Divide both sides by 4: \( x=\frac{48}{4}=12 \).

Step4: Find the length of \( AB \)

Since \( AB = 3x \), substitute \( x = 12 \): \( AB=3\times12 = 36 \).

Answer:

36 (corresponding to the option with 36)