Question

Determine whether the figures are similar.

Answer 1

The answer is c. yes; scale factor = 2/7 

The figures are similar if:
$\frac{a_1}{b_1} = \frac{a_2}{b_2} \\ \\ a_1b_2 = a_2b_1$

a1 = 4
b1 = 7
a2 = 14
b2 = 24.5

$a_1b_2 = a_2b_1 \\ \\ 4 * 24.5 = 7 * 14 \\ 98 = 98$

The figures are similar, now let's find the scale factor:
$\frac{a_1}{a_2} = \frac{4}{14} = \frac{4:2}{14:2} = \frac{2}{7} \\ \\ \frac{b_1}{b_2} = \frac{7}{24.5} = \frac{7:3.5}{24.5:3.5} = \frac{2}{7}$