Question

determine the length of ef in these similar triangles.
\\(\frac{9}{18}=\frac{16.2}{32.4}\\)
\\(16.2 \times 18 \div 9 = 32\\)

1. determine the length of bd in these similar triangles.

(image of triangle with points a, b, c, d, e; ae=20, ed=10.5, dc=7)
topics i should practice:

Explanation:

Step1: Identify similar triangles property

Since \(\triangle ABC \sim \triangle EDC\) (by AA similarity, as \(BD \parallel AE\) implies corresponding angles equal), the ratios of corresponding sides are equal. Let \(BD = x\). Then \(\frac{BD}{AE}=\frac{CD}{CE}\). \(CE = CD + DE = 7 + 10.5 = 17.5\), \(AE = 20\), \(CD = 7\).

Step2: Set up proportion

\(\frac{x}{20}=\frac{7}{17.5}\)

Step3: Solve for \(x\)

Cross - multiply: \(17.5x = 20\times7\)
\(17.5x = 140\)
\(x=\frac{140}{17.5}=8\)

Answer:

The length of \(BD\) is \(8\).