Question

Bobcat park is a rectangular park with an area of 5 1/5 square miles. Its width is 1 19/20 miles. How long is the park?

Answer 1

let's firstly convert the mixed fraction to improper fraction.

`\bf \stackrel{mixed}{5(1)/(5)}\implies \cfrac{5\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{26}{5}}\\\\\\ \stackrel{mixed}{1(19)/(20)}\implies \cfrac{1\cdot 20+19}{20}\implies \stackrel{improper}{\cfrac{39}{20}} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ w=(39)/(20)\\[1em] A=(26)/(5) \end{cases}\implies \cfrac{26}{5}=L\cdot \cfrac{39}{20}\implies \cfrac{26}{5}= \cfrac{39L}{20} \\\\\\ 520=195L\implies \cfrac{520}{195}=L\implies \cfrac{8}{3}=L\implies 2(2)/(3)=L`