Question

15 feet
b 9 feet
c 6 feet
d
x feet
e
which proportion solves for the distance between d and e?
\\( \frac{9}{6} = \frac{x}{15} \\)
\\( \frac{6}{x} = \frac{15}{9} \\)
\\( \frac{9}{6} = \frac{15}{x} \\)
\\( \frac{6}{15} = \frac{9}{x} \\)

Explanation:

Step1: Identify Similar Triangles

The triangles formed are similar (by vertical angles and corresponding angles, assuming parallel sides). So, corresponding sides are proportional.

Step2: Match Corresponding Sides

Side \( BC = 9 \) ft corresponds to side \( DC = 6 \) ft, and side \( AB = 15 \) ft corresponds to side \( DE = x \) ft.

Step3: Set Up Proportion

The proportion of corresponding sides is \( \frac{BC}{DC}=\frac{AB}{DE} \), substituting values: \( \frac{9}{6}=\frac{15}{x} \).

Answer:

\(\boldsymbol{\frac{9}{6}=\frac{15}{x}}\) (the third option, e.g., C. \(\frac{9}{6}=\frac{15}{x}\) if options are labeled A - D as such)