Question

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 \(FG\parallel CD\) in \(\triangle ECD\), we have \(\frac{EF}{FC}=\frac{EG}{GD}\).
Given \(EF = 13.3\), \(FC = 10.7\), \(EG=26.7\), and \(GD = x\).

Step2: Substitute the values into the proportion

\(\frac{13.3}{10.7}=\frac{26.7}{x}\).
Cross - multiply: \(13.3x=10.7\times26.7\).

Step3: Solve for \(x\)

First, calculate \(10.7\times26.7 = 285.69\).
Then \(x=\frac{285.69}{13.3}\).
\(x = 21.4\) (rounded to the nearest tenth).

Answer:

\(x = 21.4\)