Question

hi || gj. find hk.
hk =

Explanation:

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

Since \( \overline{HI}\parallel\overline{GJ}\), we have \(\frac{KG}{GH}=\frac{KJ}{JI}\). Let \(HK = x\), then \(KG=x - 12\). And \(KJ = 36\), \(JI=18\).

Step2: Set up the proportion equation

\(\frac{x - 12}{12}=\frac{36}{18}\)

Step3: Simplify the right - hand side of the equation

\(\frac{36}{18}=2\), so the equation becomes \(\frac{x - 12}{12}=2\)

Step4: Solve for \(x\)

Multiply both sides by \(12\): \(x-12=2\times12\), \(x - 12=24\), then \(x=24 + 12\)

Answer:

\(36\)