Question 149613
Let L=length and W=width



Since the "length of a top of a board is 6m greater than width", this means that the first equation is {{{L=W+6}}}. Also, since the "area is 72m^2", this tells us that {{{A=L*W=72}}} or {{{A=72}}}



{{{A=L*W}}} Start with the given equation.



{{{72=(W+6)*W}}} Plug in {{{A=72}}} and {{{L=W+6}}}.



{{{72=W^2+6W}}} Distribute



{{{0=W^2+6W-72}}} Subtract 72 from both sides.



Let's use the quadratic formula to solve for W



{{{W = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{W = (-(6) +- sqrt( (6)^2-4(1)(-72) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=6}}}, and {{{c=-72}}}



{{{W = (-6 +- sqrt( 36-4(1)(-72) ))/(2(1))}}} Square {{{6}}} to get {{{36}}}. 



{{{W = (-6 +- sqrt( 36--288 ))/(2(1))}}} Multiply {{{4(1)(-72)}}} to get {{{-288}}}



{{{W = (-6 +- sqrt( 36+288 ))/(2(1))}}} Rewrite {{{sqrt(36--288)}}} as {{{sqrt(36+288)}}}



{{{W = (-6 +- sqrt( 324 ))/(2(1))}}} Add {{{36}}} to {{{288}}} to get {{{324}}}



{{{W = (-6 +- sqrt( 324 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{W = (-6 +- 18)/(2)}}} Take the square root of {{{324}}} to get {{{18}}}. 



{{{W = (-6 + 18)/(2)}}} or {{{W = (-6 - 18)/(2)}}} Break up the expression. 



{{{W = (12)/(2)}}} or {{{W =  (-24)/(2)}}} Combine like terms. 



{{{W = 6}}} or {{{W = -12}}} Simplify. 



Since a negative width is not possible, the only possible width is {{{W = 6}}} 



So the width is 6 m



{{{L=W+6}}} Go back to the first equation.



{{{L=6+6}}} Plug in {{{W=6}}}



{{{L=12}}} Add



So the length is 12 m