Question

solve for be

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(DE\parallel AC\), we have \(\frac{BD}{DA}=\frac{BE}{EC}\). Here, \(BD = 4\), \(DA=8\), and \(EC = 9\). Let \(BE=x\). Then \(\frac{4}{8}=\frac{x}{9}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(8x=4\times9\). So \(8x = 36\). Then \(x=\frac{36}{8}=4.5\).

Answer:

\(4.5\)