Hi

width is half the height

Let x and x/2 represent height and width respectively

Question states***

 x(x/2) = 50 ft^2

solving for x

 x^2/2 = 50 ft^2

  x^2 = 100 ft^2

    x = ± 10  |Tossing out negative solution for length

    x = 10ft, the height of the wall.  the width is 5ft  ((1/2)*10ft) 

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