Question

The perimeter and area of a rectangular ground are 46 m and 132 m² respectively.

The longest side of the rectangular ground measures

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{longer}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{garden}=x\mathrm{m} \\ \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{shorter}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{garden}=y\mathrm{m} \\ \mathrm{now},\mathrm{perimeter}=46\mathrm{m} \\ \Rightarrow 2\left(\mathrm{longer}\mathrm{side}+\mathrm{shorter}\mathrm{side}\right)=46 \\ \Rightarrow 2\left(x+y\right)=46 \\ \Rightarrow x+y=23 \\ \Rightarrow y=23-x......\left(1\right) \\ \mathrm{Now}, \\ \mathrm{area}\mathrm{of}\mathrm{garden}=132{\mathrm{m}}^2 \\ \Rightarrow xy=132 \\ \Rightarrow x\left(23-x\right)=132\left[\mathrm{using}\left(1\right)\right] \\ \Rightarrow 23x-x^2-132=0 \\ \Rightarrow x^2-23x+132=0 \\ \Rightarrow x^2-12x-11x+132=0 \\ \Rightarrow x\left(x-12\right)-11\left(x-12\right)=0 \\ \Rightarrow \left(x-12\right)\left(x-11\right)=0 \\ \Rightarrow x-12=0orx-11=0 \\ \Rightarrow x=12orx=11\left(\mathrm{rejected},\mathrm{as}x\mathrm{is}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{longer}\mathrm{side}\right) \\ \mathrm{so},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{longer}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{garden}=12\mathrm{m} \\ \mathrm{length}\mathrm{of}\mathrm{smaller}\mathrm{side}\mathrm{of}\mathrm{garden}=23-12=11\mathrm{m} \end{gathered}$$