Question

triangles abc and def are similar. type your answers in the boxes. a. find the length of segment bc. 3.0 units b. find the length of segment df. units

Explanation:

Step1: Find the scale factor

Since the triangles are similar, the ratio of corresponding sides is equal. The ratio of \(AB\) to \(DE\) is \(\frac{AB}{DE}=\frac{3}{2}\).

Step2: Find the length of \(BC\)

We know that \(\frac{BC}{EF}=\frac{AB}{DE}\). Let \(BC = x\). Then \(\frac{x}{\frac{10}{3}}=\frac{3}{2}\). Cross - multiply: \(2x = 3\times\frac{10}{3}\). So \(2x = 10\), and \(x = 5\).

Step3: Find the length of \(DF\)

We use the ratio \(\frac{AC}{DF}=\frac{AB}{DE}\). Let \(DF=y\). Then \(\frac{7}{y}=\frac{3}{2}\). Cross - multiply: \(3y=7\times2\). So \(3y = 14\), and \(y=\frac{14}{3}\approx4.67\).

Answer:

a. \(5\) units
b. \(\frac{14}{3}\) units