​ The perimeter of a rectangle is 48 cm. It would remain unchanged if

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Your question appears to be incomplete. However if the question is 
"​ The perimeter of a rectangle is 48 cm. It would remain unchanged if the length of rectangle is twice the breadth. find the length and breadth of rectangle."

$$\begin{gathered} Let the breadth of rec\tan gle be x \\ then the length of rec\tan gle be 2x \\ Since the perimeter of rec\tan gle remained unchanged \\ \therefore perimeter of rec\tan gle=48 \\ \Rightarrow 2(L+B)=48 \\ \Rightarrow 2\left(2x+x\right)=48 \\ \Rightarrow 2\times 3x=48 \\ \Rightarrow x=\frac{48}{6} \\ \Rightarrow x=8 \\ thus, the breadth of rec\tan gle=8 \\ and length of rec\tan gle=2x=2\times 8=16 \end{gathered}$$
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