Question 1194281
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Let one dimension of the rectangle be x.<br>
Then, since the area is {{{sqrt(3)}}}, the other dimension is {{{sqrt(3)/x}}}.<br>
The diagonal has length 2, so the square of the diagonal is 4.<br>
{{{x^2+(sqrt(3)/x)^2=4}}}
{{{x^2+3/x^2=4}}}
{{{x^2-4+3/x^2=0}}}
{{{x^4-4x^2+3=0}}}
{{{(x^2-1)(x^2-3)=0}}}<br>
{{{x=1}}} or {{{x=sqrt(3)}}}  (ignore the negative solutions, since they make no sense)<br>
If x is 1, then the other dimension is sqrt(3); if x is sqrt(3), then the other dimension is 1.  Either way, the dimensions of the rectangle are 1 and sqrt(3).<br>
ANSWER: 1 by sqrt(3)<br>