Question

the table below gives the dimensions of a statue and a scale drawing of the statue. find the scale factor of the drawing. (the scale factor to get the drawing from the statue.) write your answer as a fraction in simplest form. drawing statue height (inches) 9 36 length (inches) 6 24 scale factor: \\(\frac{\square}{\square}\\)

Explanation:

Step1: Recall scale factor formula

The scale factor from the statue (original) to the drawing (scaled) is \(\frac{\text{Drawing Dimension}}{\text{Statue Dimension}}\). We can use either height or length. Let's use height first.

Step2: Calculate using height

Height of drawing is \(9\), height of statue is \(36\). So scale factor is \(\frac{9}{36}\).

Step3: Simplify the fraction

Simplify \(\frac{9}{36}\) by dividing numerator and denominator by their greatest common divisor, which is \(9\). \(\frac{9\div9}{36\div9}=\frac{1}{4}\). We can check with length: \(\frac{6}{24}=\frac{1}{4}\) (dividing numerator and denominator by \(6\)).

Answer:

\(\frac{1}{4}\)