Question

ament according to the words under each answer.
abcde ~ vwxyz

1. find the length

of dc.

1. find the length of vw.

Explanation:

Step1: Find the scale factor

Since \(ABCDE\sim VWXYZ\), the scale factor \(k\) is \(\frac{ZY}{ED}\). Given \(ZY = 5\) and \(ED=2\), then \(k=\frac{5}{2}=2.5\)

Step2: Find the length of \(DC\)

We know that \(\frac{YX}{DC}=k\). Given \(YX = 8\) and \(k = 2.5\), then \(DC=\frac{YX}{k}\)

Substitute the values: \(DC=\frac{8}{2.5}=\frac{8\times2}{2.5\times2}=\frac{16}{5} = 3.2\)

Step3: Find the length of \(VW\)

We know that \(\frac{VW}{AB}=k\). Given \(AB = 2.5\) and \(k = 2.5\)

Substitute the values: \(VW=AB\times k=2.5\times2.5 = 6.25\)

Answer:

1. The length of \(DC\) is \(3.2\)
2. The length of \(VW\) is \(6.25\)