Question

find k.

write your answer as a whole number or a decimal. do not round.
k = \boxed{} feet

Explanation:

Step1: Use the property of similar triangles

Since \(NP\parallel ML\), \(\triangle ONP\sim\triangle OML\). The ratio of corresponding sides of similar triangles is equal.
The ratio of the heights is \(\frac{30 + 15}{30}=\frac{45}{30}=\frac{3}{2}\).

Step2: Set up the proportion

Let \(k\) be the length of \(ML\). We know that \(\frac{ML}{NP}=\frac{OL}{OP}\). Substituting the values, \(\frac{k}{16}=\frac{45}{30}\).
Cross - multiply: \(30k = 16\times45\).

Step3: Solve for \(k\)

First, calculate \(16\times45=720\). Then \(k=\frac{720}{30}\).

Answer:

\(k = 24\) feet