Question

determine the scale factor from the following similar figures.
original (blue rectangle): length 40 m, width 8.5 m
new (red rectangle): length 85 m, width 18.06 m (partially visible)
multiple choice options: 1, 3, 2.125, 4

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) from original to new figure is \( k=\frac{\text{New length}}{\text{Original length}} \). We can use either the length or the width (since figures are similar, both should give same \( k \)).

Step2: Calculate using length

Original length \( = 40 \, \text{m} \), New length \( = 85 \, \text{m} \).
\( k=\frac{85}{40}=2.125 \).
(We can verify with width: Original width \( = 8.5 \, \text{m} \), New width \( = 18.06 \, \text{m} \)? Wait, no, maybe typo, should be \( 18.0625 \)? Wait \( 8.5\times2.125 = 18.0625 \), and \( 40\times2.125 = 85 \). So correct.)

Answer:

2.125 (corresponding to the option with 2.125)