Question

in the diagram below, no is parallel to kl. if lo = 16, mo = 24, and kl = 44, find the length of no. figures are not necessarily drawn to scale. state your answer in simplest radical form, if necessary.

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(NO\parallel KL\), we have \(\frac{MN}{NK}=\frac{MO}{OL}\). Let \(MO = x\), then \(OL=44 - x\). And \(MN = 16\), \(NK = 24\). So \(\frac{16}{24}=\frac{x}{44 - x}\).

Step2: Cross - multiply

Cross - multiplying gives \(16\times(44 - x)=24x\).
Expanding the left - hand side: \(16\times44-16x = 24x\).
\(704-16x = 24x\).

Step3: Solve for \(x\)

Add \(16x\) to both sides: \(704=24x + 16x\).
Combine like terms: \(704 = 40x\).
Then \(x=\frac{704}{40}=\frac{88}{5}=17.6\).

Answer:

\(17.6\)