Question

hexagon b is a scaled copy of hexagon a. hexagon a hexagon b what scale factor takes hexagon a to hexagon b?

Explanation:

Step1: Convert mixed - numbers to improper fractions

$4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}$, $8\frac{1}{2}=\frac{8\times2+1}{2}=\frac{17}{2}$, $5\frac{5}{8}=\frac{5\times8 + 5}{8}=\frac{45}{8}$, $10\frac{5}{8}=\frac{10\times8+5}{8}=\frac{85}{8}$

Step2: Calculate the scale factor using one pair of corresponding sides

Let's use the vertical sides. The scale factor $k$ is given by the ratio of the side - length of hexagon $B$ to the side - length of hexagon $A$.
$k=\frac{\frac{85}{8}}{\frac{17}{2}}$

Step3: Simplify the fraction

$k=\frac{85}{8}\div\frac{17}{2}=\frac{85}{8}\times\frac{2}{17}=\frac{85\times2}{8\times17}=\frac{170}{136}=\frac{5}{4} = 1.25$

Answer:

$1.25$