Question 1000006
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S=side of smaller room
L=S+4m=side of larger room
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{{{S^2+L^2=208m^2}}}
{{{S^2+(S+4)^2=208m^2}}}
{{{S^2+(S^2+8S+16)=208m^2}}}
{{{2S^2+8S+16=208m^2}}}
{{{S^2+4S+8=104m^2}}}
{{{S^2+4S-96=0}}}
{{{(S+12)(S-8)=0}}}
{{{S+12=0}}} {{{OR}}} {{{S-8=0}}}
{{{S=-12}}} {{{OR}}} {{{S=8}}}
Since the size cannot be negative, 
the sides of the smaller room are 8 meters.
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The sides of the larger room are S+4m = 8m+4m = 12 meters.
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CHECK: 
{{{S^2+L^2=208m^2}}}
{{{(8m)^2+(12m)^2=208m^2}}}
{{{64m^2+144m^2=208m^2}}}
{{{208m^2=208m^2}}}