Let

x = the width of the rectangle, x>0

2x = the length of the rectangle

P = 54 yd the perimeter of the rectangle

A = the area of the rectangle

First we will find the width and the length and then the area.

Since the perimeter P = 2(length + width) we can write:

2(2x + x) = 54

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x = 9 yd

2x = 2*9 = 18 yd

The area of the rectangle is A = length*width or:

A = 18*9

A = 162 yd^2

The area of the rectangle is 162 yd^2.