Question

You have 314 feet of fencing to builf a circular sheep pen. What is the largest diameter pen you can build? Use π=3.13

Answer 1

$\bf \textit{circumference/perimeter of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ C=314 \end{cases}\implies 314=\pi d\implies \cfrac{314}{\pi }=d \\\\\\ \stackrel{\textit{using }\pi =3.14}{\cfrac{314}{3.14}=d}\implies \cfrac{314}{~~\frac{314}{100}~~}=d\implies \cfrac{\underline{314}}{1}\cdot \cfrac{100}{\underline{314}}=d\implies \boxed{100=d}$