Question Number 3838 by Rasheed Soomro last updated on 22/Dec/15
$${Show}\:{that}\:{the}\:{construction}\:{of} \\ $$$$\:\:\:\:\:\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{of}\:\mathrm{minimum}\: \\ $$$$\:\:\:\:\:\:\mathrm{perimeter}\:\mathrm{when}\:\mathrm{its}\:\mathrm{area}\:\:\mathrm{is}\:\boldsymbol{\mathrm{ab}}\: \\ $$$$\:\:\:\:\:\:\mathrm{where}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{AB}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{CD}}\:\mathrm{are}\:\:\mathrm{given} \\ $$$${is}\:{possible}\:{with}\:{ruler}\:{and}\:{compass}.\:\:\:\:\: \\ $$$$ \\ $$
Commented by prakash jain last updated on 22/Dec/15
$$\mathrm{For}\:\mathrm{a}\:\mathrm{given}\:\mathrm{area}\:\mathrm{square}\:\mathrm{has}\:\mathrm{minimum} \\ $$$$\mathrm{permeter}\:\mathrm{among}\:\mathrm{rectangles}. \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{square}=\sqrt{{ab}} \\ $$
Commented by Rasheed Soomro last updated on 22/Dec/15
$$\mathcal{T}{o}\:\:\mathcal{S}{ir}\:\mathcal{P}{rakash} \\ $$$${Question}\:{is}\:{then}\:'{to}\:{show}\:{that}\:{a}\:{rectangle} \\ $$$${can}\:{be}\:{squared}\:{with}\:{ruler}\:{and}\:{compass}.' \\ $$$$\boldsymbol{\mathrm{But}}\:{you}\:{don}'{t}\:{need}\:{to}\:{do}\:{so},\:{because}\:{in} \\ $$$${answering}\:{some}\:{other}\:{questions}\:{you}\:{have} \\ $$$${already}\:{proved}\:{that}\:\boldsymbol{\mathrm{ab}}\:{can}\:{be}\:{constructed} \\ $$$${when}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{are}\:{given}\:{and}\:{also}\:{squareroot} \\ $$$${of}\:{any}\:{number}…\: \\ $$$$\mathcal{I}{f}\:{anybody}\:{else}\:{wants}\:{to}\:{try},{he}\:{can}. \\ $$
Commented by prakash jain last updated on 22/Dec/15
$$\mathrm{Answers}\:\mathrm{to}\:\mathrm{previous}\:\mathrm{question}\:\mathrm{already}\:\mathrm{show} \\ $$$$\mathrm{that}\:{ab}\:\mathrm{and}\:\sqrt{{ab}}\:\mathrm{can}\:\mathrm{be}\:\mathrm{drawn}. \\ $$
Commented by Rasheed Soomro last updated on 22/Dec/15
$$\mathcal{TH}{an}\mathcal{K}^{\mathcal{S}} ! \\ $$