Question

What is the similarity ratio of a prism with surface area 36 ft2 to a similar prism with surface area 225 ft2?

Answer 1

Answer: 6:15___{2:5}

The reduce it by dividing by 3.

6/3 =2.

15/3 =5.

= {2:5}

Answer 2

`\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{√(s^2)}{√(s^2)}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------`

`\bf \stackrel{sides}{\cfrac{s^2}{s^2}}=\stackrel{areas}{\cfrac{36}{225}}\implies \left( \cfrac{s}{s} \right)^2=\cfrac{36}{225}\implies \cfrac{s}{s}=\sqrt{\cfrac{36}{225}} \implies \cfrac{s}{s}=\cfrac{√(36)}{√(225)} \\\\\\ \cfrac{s}{s}=\cfrac{6}{15}\implies \cfrac{s}{s}=\cfrac{2}{5}\qquad \qquad \stackrel{\textit{similarity ratio}}{s~:~s\implies 2~:~5}`