Question

nearest tenth if necessary.
answer
x =

Explanation:

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

Since \(EF\parallel BC\), we have \(\frac{DE}{EB}=\frac{DF}{FC}\).

Step2: Substitute the given values

Let \(DE = x\), \(EB = 1.9\), \(DF = 2.5\), \(FC = 1.5\). Then \(\frac{x}{1.9}=\frac{2.5}{1.5}\).

Step3: Solve for \(x\)

Cross - multiply: \(1.5x=1.9\times2.5\). So \(1.5x = 4.75\). Then \(x=\frac{4.75}{1.5}\approx3.2\).

Answer:

\(x = 3.2\)