Question 394754
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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 = (-14 +- sqrt(2116))/(2) = (-14 +- 46)/(2) }}} 
 x = -30 and x = 16  |tossing out negative solution:  x = 16
the lengths of the leg are 16ft and 30ft   (16ft + 14ft)