Question

AABC~ AXYZ Find the missing side length, s S. B 6 9 A 8 Z x S Մի

Answer 1

S=12

Explanation

Step 1

as the figures are similar , the ratio of two of the sides must be equal

so

let

$\text{ratio}=\frac{biggger\text{ side}}{\text{medium side}}$

so,

Ratio 1

$\begin{gathered} \text{Ratio}_1=\frac{8}{6}=\frac{4}{3} \\ \text{Ratio}_1=\frac{4}{3} \end{gathered}$

and Ratio 2

$\text{Ratio}_2=\frac{s}{9}$

now, we can construct a proportion ( the ratios are similar, so)

$\begin{gathered} \text{Ratio}_1=Ratio_2 \\ \frac{4}{3}=\frac{s}{9} \end{gathered}$

Step 2

solve for s

$\begin{gathered} \frac{4}{3}=\frac{s}{9} \\ \text{cross multiply} \\ 4\cdot9=3\cdot s \\ 36=3s \\ \text{divide both sides by 3} \\ \frac{36}{3}=\frac{3s}{3} \\ 12=s \end{gathered}$

therefore

s=12