The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

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Let, length  = x cm 
and breadth  = y cm 
We know , Permeter 
ATQ = 2(x  +  y) : y  =  5 : 1
$$\begin{gathered} \Rightarrow 5y=2x+2y \\ \Rightarrow 5y-2y=2x \\ \Rightarrow 3y=2x \\ .\text{'}. y=\frac{2x}{3} \\ Again ATQ, \\ xy =216 \\ \Rightarrow x.\frac{2x}{3}=216 \\ \Rightarrow 2x^2=216\times 3 \\ \Rightarrow x^2=\frac{216\times 3}{2} \\ \Rightarrow x^2=324 \\ \Rightarrow x=\sqrt{324} \\ .\text{'}. x =18 cm \end{gathered}$$