# The perimeter of a rectangle is 48 cm. It would remain unchanged if

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" The perimeter of a rectangle is 48 cm. It would remain unchanged if the length of rectangle is twice the breadth. find the length and breadth of rectangle."

$Letthebreadthofrec\mathrm{tan}glebex\phantom{\rule{0ex}{0ex}}thenthelengthofrec\mathrm{tan}glebe2x\phantom{\rule{0ex}{0ex}}Sincetheperimeterofrec\mathrm{tan}gleremainedunchanged\phantom{\rule{0ex}{0ex}}\therefore perimeterofrec\mathrm{tan}gle=48\phantom{\rule{0ex}{0ex}}\Rightarrow 2(L+B)=48\phantom{\rule{0ex}{0ex}}\Rightarrow 2\left(2x+x\right)=48\phantom{\rule{0ex}{0ex}}\Rightarrow 2\times 3x=48\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{48}{6}\phantom{\rule{0ex}{0ex}}\Rightarrow x=8\phantom{\rule{0ex}{0ex}}thus,thebreadthofrec\mathrm{tan}gle=8\phantom{\rule{0ex}{0ex}}andlengthofrec\mathrm{tan}gle=2x=2\times 8=16\phantom{\rule{0ex}{0ex}}$

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