Let the sides of the rectangle be x and 343/x.
Perimeter = 2(l + w) = 2(x + 343/x) = 2x + 686/x
For minimum perimeter, dP/dx = 0
dP/dx = 2 - 686/x^2 = 0
2x^2 - 686 = 0
x^2 - 343 = 0
(x - √343)(x + √343) = 0
x = √343
Therefore, the dimensions of the rectangle is √343 and √343.
