Question

in the diagram below, \\( \overline { g h } \\) is parallel to \\( \overline { d e } \\). solve for \\( x \\). round your answer to the nearest tenth if necessary.
answer attempt 1 out of 4
\\( x = \\)

Explanation:

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

Since \( \overline{GH}\parallel\overline{DE}\), by the basic proportionality theorem, we have \(\frac{FH}{HE}=\frac{FG}{GD}\).
Substituting the given values: \(\frac{13.3}{10.7}=\frac{x}{17.8}\).

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

Cross - multiplying gives \(10.7x = 13.3\times17.8\).
First, calculate \(13.3\times17.8=236.74\).
Then, \(x=\frac{236.74}{10.7}\).

Step3: Perform the division

\(x=\frac{236.74}{10.7}\approx22.1\)

Answer:

\(x = 22.1\)