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Question Number 60647 by ajfour last updated on 23/May/19

Commented by ajfour last updated on 23/May/19

Find maximum side length of a  square circumscribing a rectangle  with sides a and b.

$${Find}\:{maximum}\:{side}\:{length}\:{of}\:{a} \\ $$$${square}\:{circumscribing}\:{a}\:{rectangle} \\ $$$${with}\:{sides}\:{a}\:{and}\:{b}. \\ $$

Commented by mr W last updated on 23/May/19

if a≠b i think  there is an unique square with  s=((a+b)/(√2))  due to symmetry.  if a=b, there are infinite squares.  the max. square has side length  s=(√2)a

$${if}\:{a}\neq{b}\:{i}\:{think} \\ $$$${there}\:{is}\:{an}\:{unique}\:{square}\:{with} \\ $$$${s}=\frac{{a}+{b}}{\sqrt{\mathrm{2}}} \\ $$$${due}\:{to}\:{symmetry}. \\ $$$${if}\:{a}={b},\:{there}\:{are}\:{infinite}\:{squares}. \\ $$$${the}\:{max}.\:{square}\:{has}\:{side}\:{length} \\ $$$${s}=\sqrt{\mathrm{2}}{a} \\ $$

Commented by ajfour last updated on 24/May/19

thank you Sir, i agree.

$${thank}\:{you}\:{Sir},\:{i}\:{agree}. \\ $$

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