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Question Number 3417 by RasheedSindhi last updated on 13/Dec/15

$$provethatamongallclosedfigures$$$$havingsameperimetercircle$$$$hasmaximumarea.$$

Commented by Filup last updated on 13/Dec/15

$$\mathrm{I}\mathrm{dont}\mathrm{understand}\mathrm{the}\mathrm{question}$$

Commented by RasheedSindhi last updated on 13/Dec/15

$$Considerclosedfigurestriangle,$$$$quadilateral,pentagon...orother$$$$closedcurvesormixtureofcurves$$$$andstraightlinesegments,all$$$$havingsameperimeter.Among$$$$alltheareasthesefigureshave$$$$thelargestistheareaofcircle.$$

Commented by 123456 last updated on 13/Dec/15

$$\mathrm{this}\mathrm{is}\mathrm{isoperemtric}\mathrm{inequality}$$$$4\pi \mathrm{A}⩽{\mathrm{L}}^2$$

Commented by Filup last updated on 13/Dec/15

$$\mathrm{Circle}\mathrm{is}\mathrm{essentially}\mathrm{an}\mathrm{\infty }-sided$$$$polygon$$

Commented by Filup last updated on 13/Dec/15

$$3-\mathrm{gon}\left(\mathrm{triangle}\right)<4-\mathrm{gon}\left(\mathrm{square}\right)$$$$4-\mathrm{gon}<5-\mathrm{gon}$$$$\mathrm{etc}$$$$\therefore n-gon<\mathrm{\infty }-gon\left(circle\right)$$

Commented by Rasheed Soomro last updated on 13/Dec/15

$$\mathcal{W}hatismeantby\mathrm{isoperemtric}\mathrm{inequality}?$$

Commented by RasheedSindhi last updated on 13/Dec/15

$$\mathcal{T}h\propto nk\mathcal{S}$$

Commented by prakash jain last updated on 13/Dec/15

$$\mathrm{isoperimetric}\mathrm{inequality}\mathrm{for}\mathrm{all}\mathrm{closed}$$$$\mathrm{plane}\mathrm{figure}$$$$4\pi \mathrm{A}⩽{\mathrm{L}}^2$$$$\mathrm{A}\mathrm{area}$$$$\mathrm{L}\mathrm{perimeter}$$$$\mathrm{equality}\mathrm{holding}\mathrm{true}\mathrm{only}\mathrm{for}\mathrm{circle}.$$

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