Question 595166
Let x = width


Since "the length of the top of a table is 6m greater then the width", we know that the length is x+6


The area is then x(x+6), but this area is 72 sq meters, so 



{{{x(x+6) = 72}}}



Now get the equation into standard form



{{{x(x+6) = 72}}}



{{{x^2+6x = 72}}}



{{{x^2+6x - 72=0}}}



and now use the quadratic formula to solve for x.



{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(6)+-sqrt((6)^2-4(1)(-72)))/(2(1))}}}


{{{x = (-6+-sqrt(36-(-288)))/(2)}}}


{{{x = (-6+-sqrt(324))/2}}}


{{{x = (-6+sqrt(324))/2}}} or {{{x = (-6-sqrt(324))/2}}}


{{{x = (-6+18)/2}}} or {{{x = (-6-18)/2}}}


{{{x = 12/2}}} or {{{x = -24/2}}}


{{{x = 6}}} or {{{x = -12}}}


Discard the negative solution to get the only solution of {{{x=6}}}


So the width is x = <font color="red">6 meters</font>


and the length is x + 6 = 6+6 = <font color="red">12 meters</font>



As a check, notice that 12 is indeed 6 greater than 6. Also 12*6 = 72. So our answers check out.