[tex] \underline{\underline{\sf{ \color{purple}{Given :} }}} [/tex]
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[tex] \underline{\underline{\sf{ \color{purple}{To\:Find :} }}} [/tex]
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[tex]\underline{\underline{\sf{ \color{purple}{Solution :} }}}[/tex]
[tex]\underline{\tt{As\:we\:know\:that,}}[/tex]
[tex]\star\:{\boxed{\sf{\purple{Area \: of \: circle} = 2 \times Area \: of \: semicircle}}}[/tex]
[tex] : \: \implies \sf{Area \: of \: circle = 2 \times 77cm^{2} }[/tex]
[tex]: \: \implies \sf{Area \: of \: circle =154 \: {cm}^{2} }[/tex]
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[tex]\underline{\tt{Now, \: we\:know\:that,}}[/tex]
[tex]\star\:{\boxed{\sf{\purple{Area \: of \: circle} = \pi r^{2}}}}[/tex]
[tex] : \: \implies \sf{ 154 = \dfrac{22}{7} \times {r}^{2} }[/tex]
[tex] : \: \implies \sf{ 7 \times 7 = {r}^{2} }[/tex]
[tex] : \: \implies \sf{ 49 = {r}^{2} }[/tex]
[tex] : \: \implies \sf{ {r}^{2} = 49 }[/tex]
[tex] : \: \implies \sf{ {r} = \sqrt{ 49} }[/tex]
[tex] : \: \implies \sf{ {r} = { 7 cm} } [/tex]
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[tex]\underline{\tt{Now, \: we\:know\:that,}}[/tex]
[tex]\star\:{\boxed{\sf{\purple{Perimeter} = \pi r + 2r }}}[/tex]
[tex] : \: \implies \sf{ Perimeter = \dfrac{22}{7} \times 7 + 2 \times 7 }[/tex]
[tex] : \: \implies \sf{ Perimeter = 22 + 14 }[/tex]
[tex] : \: \implies \sf{ Perimeter = 36 }[/tex]
[tex]\sf \therefore \: perimeter \: of \: the \: circle \: is \: 36cm[/tex]
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