Question

diagram below, \\(\overline{fg}\\) is parallel to \\(\overline{cd}\\). if \\(fe = 7.2, cf = 6\\), and \\(fg = 3.6\\), find the length of \\(\overline{cd}\\). figures are not necessarily to scale.

Explanation:

Step1: Identify Similar Triangles

Since \( \overline{FG} \parallel \overline{CD} \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle EFG \sim \triangle ECD \) (similar triangles). So, the ratios of corresponding sides are equal: \( \frac{FE}{CE} = \frac{FG}{CD} \). First, find \( CE \): \( CE = FE + CF = 7.2 + 6 = 13.2 \).

Step2: Set Up Proportion and Solve for \( CD \)

Substitute known values into the proportion: \( \frac{7.2}{13.2} = \frac{3.6}{CD} \). Cross - multiply: \( 7.2 \times CD = 13.2 \times 3.6 \). Calculate \( 13.2\times3.6 = 47.52 \). Then, \( CD=\frac{47.52}{7.2}=6.6 \).

Answer:

\( 6.6 \)