Question

1. abcd ~ nmpo

written as a fraction, the scale factor =
x =

Explanation:

Step1: Find the scale factor

Since \(ABCD\sim NMPO\), the scale factor \(k\) is the ratio of corresponding sides. Let's take \(AB = 4\) and \(NM=2.4\).
The scale factor \(k=\frac{NM}{AB}\)
\(k = \frac{2.4}{4}=\frac{24}{40}=\frac{3}{5}\)

Step2: Use the scale factor to find \(x\)

We know that \(\frac{NM}{AB}=\frac{PO}{CD}\). Given \(CD = 6\), \(NM = 2.4\), \(AB = 4\) and \(PO=x\)
Since the scale factor \(k=\frac{3}{5}\), and \(\frac{x}{6}=\frac{3}{5}\)
Cross - multiply: \(5x=3\times6\)
\(5x = 18\)
\(x=\frac{18}{5}=3.6\)

Answer:

The scale factor is \(\frac{3}{5}\), \(x = 3.6\)