Question

in the diagram, lines bc and de are both vertical. what is the length of ad? type your answer in the box. units

Explanation:

Step1: Use the property of similar triangles

Since \(BC\parallel DE\), \(\triangle ABC\sim\triangle ADE\). For similar triangles, the ratios of corresponding sides are equal. That is \(\frac{AB}{AD}=\frac{BC}{DE}\). Let \(AD = x\), then \(AB=2\), \(BC = 3\), \(DE=4\).

Step2: Substitute values into the proportion

Substitute the values into \(\frac{AB}{AD}=\frac{BC}{DE}\), we get \(\frac{2}{x}=\frac{3}{3 + 4}\). Cross - multiply: \(3x=2\times(3 + 4)\).

Step3: Solve the equation

\(3x=2\times7\), \(3x = 14\), \(x=\frac{14}{3}\).

Answer:

\(\frac{14}{3}\)