Question

The perimeter of two square are 60 metres and 144 metres respectively . Find the perimeter of another square equal in area to the sum of thew first two square .

Answer 1

Dear student,

$$\begin{gathered} weknow,Perimeterofsquare=4\times side \\ PerimeterofIstsquare=60m \\ \Rightarrow 4\times s_1=60where,s_{1}isthesideofIstsquare \\ \Rightarrow s_1=\frac{60}{4}=15m \\ \therefore AreaofIstsquare={\left(side\right)}^2={\left(s_1\right)}^2={\left(15\right)}^2=15\times 15=225m^2 \\ Similarly,PerimeterofIIndsquare=144m \\ \Rightarrow 4\times s_2=144where,s_{2}isthesideofIIndsquare \\ \Rightarrow s_2=\frac{144}{4}=36m \\ \therefore AreaofIIndsquare={\left(side\right)}^2={\left(s_2\right)}^2={\left(36\right)}^2=36\times 36=1296m^2 \\ Giventhat:Areaofanothersquare=AreaofIstsquare+AreaofIIndsquare \\ =225m^2+1296m^2 \\ \Rightarrow Areaofanothersquare=1521m^2 \\ i.e.s_3\times s_3=1521m^{2}where,s_{3}isthesideofanothersquare \\ \Rightarrow s_3=\sqrt{1521}=39m \\ Thus,theperimeterofanothersquare=4\times s_3=4\times 39=156m \end{gathered}$$
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