Question

Rahul jogs around a square park of area p^​2-10p+25.How much distance will he cover in 2 rounds?

Answer 1

Hi
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{square}\mathrm{park}={\mathrm{p}}^2-10\mathrm{p}+25={\mathrm{p}}^2-2\times 5\times \mathrm{p}+5^2 \\ ={\left(\mathrm{p}-5\right)}^2\mathrm{square}\mathrm{unit} \\ {\mathrm{side}}^2={\left(\mathrm{p}-5\right)}^2\mathrm{square}\mathrm{unit} \\ \mathrm{side}=\left(\mathrm{p}-5\right)\mathrm{unit} \\ \mathrm{so}\mathrm{perimeter}=\mathrm{distance}\mathrm{covered}\mathrm{in}\mathrm{a}\mathrm{round} \\ \mathrm{so}\mathrm{distance}\mathrm{covered}\mathrm{in}\mathrm{two}\mathrm{rounds}=2\times \mathrm{perimeter}\mathrm{of}\mathrm{square}\mathrm{park} \\ =2\times 4\times \left(\mathrm{p}-5\right)\mathrm{unit} \\ =\left(8\mathrm{p}-40\right)\mathrm{unit} \end{gathered}$$