Question

1. if the figures below are similar, find the scale factor of figure b to figure a.

Explanation:

Step1: Find the ratio of corresponding sides

For similar figures, the scale factor is the ratio of a side length of the second figure (Figure B) to the corresponding side length of the first figure (Figure A).
We can use the pairs of sides \(27\) and \(9\), \(48\) and \(16\), \(60\) and \(20\).
Let's take the pair \(27\) (from Figure A) and \(9\) (from Figure B). The ratio is \(\frac{9}{27}\).

Step2: Simplify the ratio

Simplify \(\frac{9}{27}\) by dividing both the numerator and the denominator by their greatest - common divisor, which is \(9\).
\(\frac{9\div9}{27\div9}=\frac{1}{3}\).
We can check with another pair: \(\frac{16}{48}=\frac{16\div16}{48\div16}=\frac{1}{3}\), and \(\frac{20}{60}=\frac{20\div20}{60\div20}=\frac{1}{3}\)

Answer:

The scale factor of Figure B to Figure A is \(\frac{1}{3}\)