Question

de || ac
find the length of \\(\overline{da}\\).
\\(da = \square\\)

Explanation:

Step1: Apply Basic Proportionality Theorem (Thales' theorem)

Since \( DE \parallel AC \), by Thales' theorem, \(\frac{BD}{DA}=\frac{BE}{EC}\).
Given \( BD = 7 \), \( BE = 8 \), \( EC = 12 \), let \( DA = x \). So we have \(\frac{7}{x}=\frac{8}{12}\).

Step2: Solve the proportion for \( x \)

Cross - multiply: \( 8x=7\times12 \).
Calculate \( 7\times12 = 84 \), so \( 8x = 84 \).
Then \( x=\frac{84}{8}=\frac{21}{2}=10.5 \).

Answer:

\( 10.5 \) (or \(\frac{21}{2}\))