Question 1189792
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x = side length of the planted area (ie we ignore the walkway)


When considering the walkway, we add on 3+3 = 6 feet for each dimension of the square.
The x by x square bumps up to (x+6) by (x+6)


The larger square has area of 
(x+6)^2
(x+6)*(x+6)
x(x+6)+6(x+6)
x^2+6x+6x+36
x^2+12x+36


Set this area expression equal to the desired area (18,000) and solve for x.
x^2+12x+36 = 18,000
x^2+12x+36-18,000 = 0
x^2+12x-17,964 = 0


Now turn to the quadratic formula
{{{x = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x = (-(12)+-sqrt((12)^2-4(1)(-17964)))/(2(1))}}}


{{{x = (-12+-sqrt(72000))/(2)}}}


{{{x = (-12+-268.3281573)/(2)}}}


{{{x = (-12+268.3281573)/(2)}}} or {{{x = (-12-268.3281573)/(2)}}}


{{{x = (256.3281573)/(2)}}} or  {{{x = (-280.32815728)/(2)}}}


{{{x = 128.16407865}}} or  {{{x = -140.16407863}}}


We ignore the negative x value because we cannot have negative side lengths.


The square planted area is roughly 128.16 feet by 128.16 feet.


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Here's another way to solve.


We start off with some smaller square representing the plants only. Adding on the walkway of uniform with around all the edges will get us some larger square.


Let's say this larger square has side lengths of W. So W^2 is the area of this larger square.
Set it equal to the 18,000 figure and solve for W


{{{W^2 = 18000}}}


{{{W = sqrt(18000)}}}


{{{W = 134.164079}}}


The side lengths of the larger square are roughly 134.164079 feet


We then subtract off 6 feet due to the 3+3 = 6 figure calculated earlier
134.164079 - 6 = 128.164079


We get the same result of 128.16 as earlier.


Depending on your preferences, this option may be much easier compared to the last method.
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