Question Number 50744 by Necxx last updated on 19/Dec/18
$${If}\:{the}\:{perimeter}\:{of}\:{a}\:{rectangle}\:{is} \\ $$$${a}\:\mathrm{2}−{digit}\:{number}\:{which}\:{unit}\:{digit}\mathscr{L} \\ $$$${and}\:{tens}\:{digit}\:{represents}\:{its}\:{length} \\ $$$${and}\:{breadth}\:{respectively}.{Find}\:{its} \\ $$$${area}\:{in}\:{constant}. \\ $$
Answered by Rasheed.Sindhi last updated on 19/Dec/18
$${Let}\:{u}\:\&\:{v}\:{are}\:{length}\:\&\:{breadth}\:{respectively}. \\ $$$$\therefore\:{The}\:{perimeter}\:{is}\:\mathrm{10}{v}+{u}\:. \\ $$$${In}\:{another}\:{way}\:{this}\:{perimeter}\:=\mathrm{2}{u}+\mathrm{2}{v} \\ $$$$\:\:\:\therefore\:\mathrm{10}{v}+{u}=\mathrm{2}{u}+\mathrm{2}{v} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{8}{v}={u} \\ $$$${As}\:\:\:\mathrm{1}\leqslant{u},{v}\leqslant\mathrm{9}\:\left({any}\:{of}\:{dimension}\right. \\ $$$$\left.{can}'{t}\:{be}\:{zero}\right) \\ $$$${Hence}\:{v}\left({bre}\right)=\mathrm{1}\:\&\:{u}\left({len}\right)=\mathrm{8} \\ $$$$\left({For}\:{v}>\mathrm{1}\Rightarrow{u}>\mathrm{9}\:{i}-{e}\:{not}\:{a}\:{single}\:{digit}.\right. \\ $$$$\left.{I}-{E}\:{u}\:{is}\:{single}\:{digit}\:{only}\:{when}\:{v}=\mathrm{1}\right) \\ $$$$ \\ $$$${Perimeter}:\mathrm{18}\:,\:\:{Area}:\mathrm{8} \\ $$
Commented by Necxx last updated on 19/Dec/18
$${wow}...{mr}\:{Rasheed}\:{sindhi}\:{welcome} \\ $$$${and}\:{thanks}\:{for}\:{helping}. \\ $$
Commented by Rasheed.Sindhi last updated on 20/Dec/18
$$\theta{anks}\:{Sir}!\:{Happy}\:{to}\:{see}\:{that}\:{you}'{ve} \\ $$$${not}\:{forgotten}\:{old}\:{friends}! \\ $$