The ratio of cats to dogs is 4:5, and we can express this ratio like this:
[tex]\frac{Cats}{\text{Dogs}}=\frac{4}{5}[/tex]Now, we can solve for cats, like this:
[tex]\begin{gathered} \text{Dogs}\times\frac{Cats}{\text{Dogs}}=\frac{4}{5}\text{Dogs} \\ \text{Cats}\times\frac{Dogs}{\text{Dogs}}=\frac{4}{5}\text{Dogs} \\ \text{Cats}\times1=\frac{4}{5}\text{Dogs} \\ \text{Cats}=\frac{4}{5}\text{Dogs} \end{gathered}[/tex]And we can express the total number of animals like this:
[tex]\begin{gathered} Dogs+Cats=Animals=27 \\ \end{gathered}[/tex]We can replace cats, and find the value of Dogs like this:
[tex]\begin{gathered} \text{Dogs}+\text{Cats}=27 \\ \text{Dogs}+\frac{4}{5}\text{Dogs}=27 \\ \text{Dogs}(1+\frac{4}{5})=27 \\ \text{Dogs}\frac{4+5}{4}=27 \\ \text{Dogs}\frac{9}{5}=27 \\ \text{Dogs}\frac{9}{5}\times\frac{5}{9}=27\times\frac{5}{9} \\ \text{Dogs}=\frac{27\times5}{9}=\frac{135}{9}=15 \end{gathered}[/tex]And as the total amount of dogs is 15 and we use 5 small rectangles to represent them, we can find the value of each rectangle like this:
[tex]\text{value of each regtangle=}\frac{15}{5}=3[/tex]