<PRE><B>Question 148258</B>
Let x=amount he increased the dimensions of his garden, {{{A[o]}}}=area of original garden and  {{{A[n]}}}=area of new garden

Since the original garden is 12 ft by 14 ft, this means that the area of the original garden is


{{{A[o]=12*14=168}}}


So {{{A[o]=168}}} which means that the area of the original garden is 168 ft^2



Because the area of the new garden is 120 ft^2 larger than the original garden, this means that {{{A[n]=A[o]+120}}}



{{{A[n]=168+120}}} Plug in {{{A[o]=168}}}



{{{A[n]=288}}} Add



So the area of the new garden is 288 ft^2



Now since he increased the dimensions by some unknown amount, this means that the area of the new garden is equal to:


{{{A[n]=(12+x)(14+x)}}}



{{{288=(12+x)(14+x)}}} Plug in {{{A[n]=288}}}



{{{288=168+26x+x^2}}} FOIL



{{{0=168+26x+x^2-288}}} Subtract 288 from both sides.



{{{0=x^2+26x-120}}} Combine and rearrange the terms.



Let&#39;s use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(26) +- sqrt( (26)^2-4(1)(-120) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=26}}}, and {{{c=-120}}}



{{{x = (-26 +- sqrt( 676-4(1)(-120) ))/(2(1))}}} Square {{{26}}} to get {{{676}}}. 



{{{x = (-26 +- sqrt( 676--480 ))/(2(1))}}} Multiply {{{4(1)(-120)}}} to get {{{-480}}}



{{{x = (-26 +- sqrt( 676+480 ))/(2(1))}}} Rewrite {{{sqrt(676--480)}}} as {{{sqrt(676+480)}}}



{{{x = (-26 +- sqrt( 1156 ))/(2(1))}}} Add {{{676}}} to {{{480}}} to get {{{1156}}}



{{{x = (-26 +- sqrt( 1156 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-26 +- 34)/(2)}}} Take the square root of {{{1156}}} to get {{{34}}}. 



{{{x = (-26 + 34)/(2)}}} or {{{x = (-26 - 34)/(2)}}} Break up the expression. 



{{{x = (8)/(2)}}} or {{{x =  (-60)/(2)}}} Combine like terms. 



{{{x = 4}}} or {{{x = -30}}} Simplify. 



So the possible answers are {{{x = 4}}} or {{{x = -30}}} 

  

However, since a negative length is not possible, this means that he increased his garden by 4 feet.



Now simply add 4 to each dimension 12 and 14 to get:


12+4=16  by 14+4=18


So the dimensions of the new garden are


16 ft by 18 ft



note: the approximate answers are the same as the exact answers since there are no square roots, fractions, decimals, etc. in the answer


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