Question

jk || gl. find ij.

Explanation:

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

Since \( \overline{JK}\parallel\overline{GI}\), we have the proportion \(\frac{HI}{IJ}=\frac{HG}{GK}\). Let \(IJ = x\). Here, \(HI = 13\), \(HG=20\), and \(GK = 40\).

Step2: Substitute values into the proportion

Substituting the values into \(\frac{HI}{IJ}=\frac{HG}{GK}\), we get \(\frac{13}{x}=\frac{20}{40}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(20x=13\times40\). Then \(x=\frac{13\times40}{20}\).

Step4: Simplify the expression

Simplify \(\frac{13\times40}{20}\). Since \(\frac{40}{20}=2\), then \(x = 13\times2=26\).

Answer:

\(26\)