Question

question 18 of 50
the value of k is:
diagram with parallel lines, transversals, segments labeled 24, 32, 64, and k
options: 64, 56, 32, 48, none of the choices are correct

Explanation:

Step1: Identify the theorem

This is a case of parallel lines cut by transversals, so we use the Basic Proportionality Theorem (Thales' theorem), which states that if a set of parallel lines cuts two transversals, then they divide the transversals proportionally. So, \(\frac{24}{k}=\frac{32}{64}\).

Step2: Solve for \(k\)

Cross - multiply the proportion: \(32\times k = 24\times64\). Then, \(k=\frac{24\times64}{32}\). Simplify the right - hand side: \(64\div32 = 2\), so \(k = 24\times2=48\).

Answer:

48 (and the option corresponding to 48, which is "48" among the given options)