Hi

one leg is 14ft longer than the other leg

Let x and (x+14) represent the lengths of the legs

Applying the Pytahgorean Theore,

x^2 + (x+14ft)^2 = (34ft)^2

solving for x

   2x^2 + 28x + 196 = 1156

   2x^2 + 28x - 960 =  0

   x^2 + 14z - 480 = 0

 

 x = -30 and x = 16  |tossing out negative solution:  x = 16

the lengths of the leg are 16ft and 30ft   (16ft + 14ft) 

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