Question 985366
The area of a rectangle is 
{{{Area = Width*Length}}}
You are told
{{{(5 + sqrt(3)) = Width * (2 + sqrt(3))}}}
{{{(5+sqrt(3))/(2+sqrt(3)) = Width}}}

Now rationalize the denominator
{{{((5+sqrt(3))/(2+sqrt(3))) ((2-sqrt(3))/(2-sqrt(3))) = Width}}}
{{{((5+sqrt(3)) (2-sqrt(3))) / ((2+sqrt(3)) (2-sqrt(3))) = Width}}}
{{{((10 -5sqrt(3) + 2sqrt(3) -3 ) / (4 - 3)) = Width}}}
{{{(7 -3sqrt(3)) = Width}}}

Verify your answer by multiplying {{{ (7 -3sqrt(3))}}} and {{{ 2 + sqrt(3))}}}