Question

in the diagram below, \\(\overline{de}\\) is parallel to \\(\overline{ab}\\). \\(ce = 5\\), \\(da = 3.8\\), and \\(eb = 3\\). find the length of \\(\overline{cd}\\). round your answer to the nearest tenth if necessary.

answer attempt 1 out of 2
\\(cd = \square\\) submit answer

Explanation:

Step1: Apply Basic Proportionality Theorem

Since \( \overline{DE} \parallel \overline{AB} \), by the Basic Proportionality Theorem (Thales' theorem), we have \( \frac{CD}{DA}=\frac{CE}{EB} \).

Step2: Substitute known values

We know \( CE = 5 \), \( DA = 3.8 \), and \( EB = 3 \). Let \( CD = x \). Then the proportion becomes \( \frac{x}{3.8}=\frac{5}{3} \).

Step3: Solve for \( x \)

Cross - multiply to get \( 3x=5\times3.8 \). Calculate \( 5\times3.8 = 19 \), so \( 3x = 19 \). Then \( x=\frac{19}{3}\approx6.3 \) (rounded to the nearest tenth).

Answer:

\( 6.3 \)