In a rectangle ABCD , a semicircle AED is cut out from the side AD. CD = 20 cm BC = 14 cm. find the perimeter of the remaining portion.
options:-
(a) 54 cm
(b) 76 cm
(c) 86 cm
(d) 66 cm.

Dear student,

Please find below the solution to the asked query:

$\mathrm{The} \mathrm{figure} \mathrm{is} \mathrm{shown} \mathrm{below}:$



$$\begin{gathered} \mathrm{Here} \mathrm{the} \mathrm{diameter} \mathrm{of} \mathrm{the} \mathrm{semicircle} \mathrm{AED} \mathrm{is} \mathrm{AD} \\ \mathrm{Since} \mathrm{ABCD}\hspace{0.17em}\mathrm{is} \mathrm{rectangle} , \mathrm{AD}=\mathrm{BC}=14 \mathrm{cm}. \\ \mathrm{So} \mathrm{the} \mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{semicircle} \mathrm{AED} \mathrm{is} \mathrm{r}=7 \mathrm{cm} \\ \mathrm{The} \mathrm{perimeter} \mathrm{of} \mathrm{semi} \mathrm{circle} \mathrm{is} \\ \frac{1}{2}\times 2\mathrm{\pi r}=\mathrm{\pi r} \\ =\frac{22}{7}\times 7 \\ =22 \mathrm{cm} \\ \mathrm{So} \mathrm{the} \mathrm{required} \mathrm{perimter} \mathrm{of} \mathrm{the} \mathrm{remaining} \mathrm{portion} \mathrm{is}, \\ \mathrm{permieter} \mathrm{of} \mathrm{semicircle}+\mathrm{AB}+\mathrm{BC}+\mathrm{CD} \\ =22+20+14+20 \\ =\mathbf{76}\mathbf{ }\mathbf{cm} \end{gathered}$$

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