Question

If the area of a semicircle is 77cm² then find its perimeter.​

Answer 1

`\underline{\underline{\sf{ \color{purple}{Given :} }}}`

• Area of the semicircle = 77 cm²

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`\underline{\underline{\sf{ \color{purple}{To\:Find :} }}}`

• Perimeter of the circle

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`\underline{\underline{\sf{ \color{purple}{Solution :} }}}`

`\underline{\tt{As\:we\:know\:that,}}`

`\star\:{\boxed{\sf{\purple{Area \: of \: circle} = 2 * Area \: of \: semicircle}}}`

`: \: \implies \sf{Area \: of \: circle = 2 * 77cm^(2) }`

`: \: \implies \sf{Area \: of \: circle =154 \: {cm}^(2) }`

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`\underline{\tt{Now, \: we\:know\:that,}}`

`\star\:{\boxed{\sf{\purple{Area \: of \: circle} = \pi r^(2)}}}`

`: \: \implies \sf{ 154 = (22)/(7) * {r}^(2) }`

`: \: \implies \sf{ 7 * 7 = {r}^(2) }`

`: \: \implies \sf{ 49 = {r}^(2) }`

`: \: \implies \sf{ {r}^(2) = 49 }`

`: \: \implies \sf{ {r} = √( 49) }`

`: \: \implies \sf{ {r} = { 7 cm} }`

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`\underline{\tt{Now, \: we\:know\:that,}}`

`\star\:{\boxed{\sf{\purple{Perimeter} = \pi r + 2r }}}`

`: \: \implies \sf{ Perimeter = (22)/(7) * 7 + 2 * 7 }`

`: \: \implies \sf{ Perimeter = 22 + 14 }`

`: \: \implies \sf{ Perimeter = 36 }`

`\sf \therefore \: perimeter \: of \: the \: circle \: is \: 36cm`

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