let x = the length and y equal the width.
the area of the plot is x * y
the perimeter of the plot is 2x + 2y, or: 2 * (x + y)
if you want the length of the plot to be equal to triple the width, then set x = 3y
the area of the plot becomes 3y * y = 3y^2.
the perimeter of the plot becomes 2 * (3y + y) = 2 * 4y = 8y
if you want the perimeter of the plot to be equal to 32 feet, then your two equations would be:
2 * (x + y) = 32
x = 3y
replace x in the first equation with 3y to get:
2 * (3y + y) = 32
simplify to get 8y = 32
solve for y to get y = 4
solve for x to get x = 3*4 = 12
the dimensions of the plot would have a length of 12 and a width of 4.
the perimeter of the plot would be 2 * (12 + 4) = 2 * 16 = 32.
the backyard measures 12 by 12.
since the length of your plot is 12 and the width of your plot is 4, then you can get 3 plots of (4 by 12) each in the 12 by 12 back yard.
they would be layed out something like this:
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