Question

calculating scale factor using the perimeters
the perimeter of the original figure is 68 feet and the perimeter of the scale drawing is 17 feet. what is the scale factor of
the reduction?

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) is given by the ratio of the perimeter of the scale - drawing (\(P_{s}\)) to the perimeter of the original figure (\(P_{o}\)), i.e., \(k=\frac{P_{s}}{P_{o}}\)

Step2: Substitute the given values

We are given that \(P_{o} = 68\) feet and \(P_{s}=17\) feet.
Substitute these values into the formula: \(k=\frac{17}{68}\)

Step3: Simplify the fraction

Simplify \(\frac{17}{68}\) by dividing both the numerator and the denominator by 17. \(\frac{17\div17}{68\div17}=\frac{1}{4}\)

Answer:

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