Question

find the value of c.

Explanation:

Step1: Apply the property of similar - triangles or the basic proportionality theorem (Thales' theorem)

Since the lines are parallel, we can set up a proportion. If we consider the segments divided by the parallel lines, we have the proportion \(\frac{11}{c}=\frac{8}{32}\).

Step2: Cross - multiply to solve for \(c\)

Cross - multiplying gives us \(8c = 11\times32\).
First, calculate \(11\times32=352\). So, \(8c = 352\).
Then, divide both sides by \(8\): \(c=\frac{352}{8}\).

Answer:

\(c = 44\)