Question

the table below gives the dimensions of a painting and a scale drawing of the painting. find the scale factor of the drawing. (the scale factor to get the drawing from the painting.) write your answer as a fraction in simplest form.
painting drawing
length (inches) 48 6
width (inches) 40 5
scale factor:

Explanation:

Step1: Calculate scale factor using length

The formula for scale factor \(k\) is \(k=\frac{\text{dimension of drawing}}{\text{dimension of painting}}\). Using length: \(k = \frac{6}{48}\)
Simplify \(\frac{6}{48}=\frac{6\div6}{48\div6}=\frac{1}{8}\)

Step2: Verify using width

Using width: \(k=\frac{5}{40}\)
Simplify \(\frac{5}{40}=\frac{5\div5}{40\div5}=\frac{1}{8}\)

Answer:

\(\frac{1}{8}\)