Question

what is the length of \\(overline{aj}\\) if \\(overline{ab} \parallel overline{jk}\\)?
8 in.
8.75 in.
10.25 in.
14 in.

Explanation:

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

Since \( \overline{AB}\parallel\overline{JK}\), we have \(\frac{HA}{AJ}=\frac{HB}{BK}\). Let \(AJ = x\). Then \(HA = 5.25\), \(HB = 3\), \(BK = 5\). The proportion is \(\frac{5.25}{x}=\frac{3}{5}\).

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

Cross - multiplying gives \(3x=5.25\times5\). So \(3x = 26.25\).

Step3: Divide both sides by 3

\(x=\frac{26.25}{3}=8.75\)

Answer:

8.75 in.