let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A rectange is twice as long as it is wide

l = 2w

It's area is 72

l*w = 72

plug l = 2w into the last equation

2w*w = 72

by solving the quadratic equation we find

w = 6

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l = 2*w = 2*6 = 12

the perimeter of rectangle is P = 2(l + w)

P = 2(12 + 6)

P = 36

the perimeter is 36.