Question

hi || gj. find gk.
gk =
submit

Explanation:

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

Since \(\overline{HI}\parallel\overline{GJ}\), we have \(\frac{IJ}{IK}=\frac{GK}{HK}\). Here, \(IJ = 36\), \(IK=36 + 54=90\), and \(HK = 36\). Let \(GK=x\). Then the proportion is \(\frac{36}{90}=\frac{x}{36}\).

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

Cross - multiplying gives \(90x=36\times36\). So \(x=\frac{36\times36}{90}\).
Simplify \(\frac{36\times36}{90}=\frac{36\times2}{5}\) (dividing numerator and denominator by \(18\)) \(=\frac{72}{5}=14.4\)

Answer:

\(14.4\)