Question

triangles abc and def are similar.
a. find the length of segment df:
b. find the length of segment ef:

Explanation:

Step1: Find the scale factor

Since \(\triangle ABC\sim\triangle DEF\), the scale factor \(k=\frac{DE}{AB}\). Given \(AB = 2\) and \(DE=1.34\), then \(k=\frac{1.34}{2}=0.67\).

Step2: Calculate the length of \(DF\)

We know that \(AC = 4\). Using the property of similar triangles \(\frac{DF}{AC}=k\). Substitute \(k = 0.67\) and \(AC = 4\) into the formula: \(DF=k\times AC\). So \(DF=0.67\times4 = 2.68\).

Step3: Calculate the length of \(EF\)

We know that \(BC = 3\). Using the property of similar triangles \(\frac{EF}{BC}=k\). Substitute \(k = 0.67\) and \(BC = 3\) into the formula: \(EF=k\times BC\). So \(EF=0.67\times3=2.01\).

Answer:

a. \(2.68\)
b. \(2.01\)