x^2=1144
x=33.82306905
the perimeter distance is the same no matter what, above is a square solution. As the width or length get longer, the opposite side gets skinner. Not sure what you mean by the "smallest" perimeter. Normally these types of problems give you the length of one side, the relation of the other side to the first, and then the total area.
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When the area of a square is 36cm2, its perimeter is: 24 cm
A square with a perimeter of 24 cm has an area of: 36 cm2
Perimeter = 24 cm so length of each side = 24/4 = 6 cm and so area = 6 cm * 6 cm = 36 cm2
A rectangle with sides of 1cm and 6cm has an area of 6 cm2 and a perimeter of 14 cm. A rectangle with sides of 2cm and 3cm has the same area but its perimeter is 10 cm.
Area = 289 sq cm so length of side = sqrt(289) = 17 cm Then perimeter = 4*side = 4*17 = 68 cm