Question 129827
Let {{{a=x}}} (ie let the first leg be represented by the unknown variable)


Since one leg is 14 ft longer than the other leg, this means {{{b=x+14}}}


{{{a^2+b^2=c^2}}} Start with pythagorean's theorem


{{{x^2+(x+14)^2=34^2}}} Plug in {{{a=x}}}, {{{b=x+14}}}, and {{{c=34}}}



{{{x^2+(x+14)^2=1156}}} Square 34 to get 1156


{{{x^2+x^2+28x+196=1156}}} Foil {{{x+14}}} to get {{{x^2+28x+196}}}


{{{x^2+x^2+28x+196-1156=0}}} Subtract 1156 from both sides 


{{{2x^2+28x-960=0}}} Combine like terms


{{{2x^2+28x-960=0}}} Start with the given equation


{{{2(x+30)(x-16)=0}}} Factor the left side 



Now set each factor equal to zero:

{{{x+30=0}}} or  {{{x-16=0}}} 


{{{x=-30}}} or  {{{x=16}}}    Now solve for x in each case



So our answer is 

 {{{x=-30}}} or  {{{x=16}}} 


However, since a negative length doesn't make any sense, our only solution is 


{{{x=16}}} 



So the first leg is 16 ft



Now simply add 14 to 16 to get the length of the other leg


{{{16+14=30}}}



So the second leg is 30 ft