Question 200795
Let L=length of garden and W=width of garden



Since the garden is "4m longer than it is wide", this tells us that {{{L=W+4}}}


Now remember, the area of any rectangle is {{{A=LW}}}



{{{A=LW}}} Start with the area of a rectangle formula



{{{96=(W+4)W}}} Plug in {{{A=96}}} (the given area) and {{{L=W+4}}}



{{{96=W(W+4)}}} Rearrange the terms.



{{{96=W^2+4W}}} Distribute



{{{0=W^2+4W-96}}} Divide



Notice that the quadratic {{{W^2+4W-96}}} is in the form of {{{AW^2+BW+C}}} where {{{A=1}}}, {{{B=4}}}, and {{{C=-96}}}



Let's use the quadratic formula to solve for "W":



{{{W = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{W = (-(4) +- sqrt( (4)^2-4(1)(-96) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=4}}}, and {{{C=-96}}}



{{{W = (-4 +- sqrt( 16-4(1)(-96) ))/(2(1))}}} Square {{{4}}} to get {{{16}}}. 



{{{W = (-4 +- sqrt( 16--384 ))/(2(1))}}} Multiply {{{4(1)(-96)}}} to get {{{-384}}}



{{{W = (-4 +- sqrt( 16+384 ))/(2(1))}}} Rewrite {{{sqrt(16--384)}}} as {{{sqrt(16+384)}}}



{{{W = (-4 +- sqrt( 400 ))/(2(1))}}} Add {{{16}}} to {{{384}}} to get {{{400}}}



{{{W = (-4 +- sqrt( 400 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{W = (-4 +- 20)/(2)}}} Take the square root of {{{400}}} to get {{{20}}}. 



{{{W = (-4 + 20)/(2)}}} or {{{W = (-4 - 20)/(2)}}} Break up the expression. 



{{{W = (16)/(2)}}} or {{{W =  (-24)/(2)}}} Combine like terms. 



{{{W = 8}}} or {{{W = -12}}} Simplify. 



So the <i>possible</i> solutions are {{{W = 8}}} or {{{W = -12}}} 



However, you can't have a negative width. So the only solution is {{{W=8}}}


So the width of the garden is 8 m. 



Now add 4 m to 8m to get 4+8=12 m. So the length is 12 m



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Answer:



So the length and width of the garden are 12 meters and 8 meters.