Question

find k.
write your answer as a whole number or a decimal. do not round.
k = meters

Explanation:

Step1: Use the similarity of triangles

Since \(NL\parallel OP\), \(\triangle MNL\sim\triangle MOP\). The ratio of corresponding sides of similar triangles is equal.
The ratio of the heights of \(\triangle MNL\) and \(\triangle MOP\) is \(\frac{ML}{MP}=\frac{3}{3 + 3}=\frac{3}{6}=\frac{1}{2}\).

Step2: Set up the proportion for the bases

Let \(NL = 4\) and \(OP=k\). Using the property of similar - triangles \(\frac{NL}{OP}=\frac{ML}{MP}\). Substituting the values, we get \(\frac{4}{k}=\frac{3}{6}\).
Cross - multiply: \(3k=4\times6\).

Step3: Solve for \(k\)

\(3k = 24\), then \(k=\frac{24}{3}\).

Answer:

\(k = 8\) meters