Question 1067790
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The gardener/the fence has 3 times the length L and 2 times the width W (it is the FULL wide, not its half).

So the equations are

3L + 2W = 100,       (1)
L*W = 336.           (2)


From (1), W = {{{(100-3L)/2}}}. Substitute it into (2) replacing W. You will get

{{{L*(100-3L)/2}}} = 336,   or

L*(100-3L) = 672,

100L - 3L^2 = 672,

3L^2 - 100L + 672 = 0.


{{{L[1,2]}}} = {{{(100 +- sqrt(100^2-4*3*672))/(2*3)}}} = {{{(100 +- 44)/6}}}.


{{{L[1]}}} = {{{144/6}}} = 24         --->  {{{W[1]}}} = {{{(100-3*24)/2}}} = 14.


{{{L[2]}}} = {{{56/6}}} = {{{9}}}{{{1/3}}}         --->  {{{W[2]}}} = {{{(100-3*(28/3))/2}}} = 36.


<U>Answer</U>.  There are two solutions: 1) the rectangle has the outer dimensions 24 m and 14 m;

                                  2) the rectangle has the outer dimensions {{{9}}}{{{1/3}}} m and 36 m.
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