Question 926757
Let width be w cm
length  = (w+14) cm
Diagonal = 34 cm
As per pythagorean theorem ,
              {{{ diagonal^2 =length^2+width^2)}}}
           {{{ 34^2 =(w+14)^2+w^2}}}
           {{{ 1156 =(w+14)*(w+14) +w^2}}}
          {{{1156  =w(w+14)+14(w+14)+w^2}}}
          {{{ 1156  = w^2+14w+14w+196+w^2}}}
          {{{ 1156 = w^2+28w +196+w^2}}}
         {{{1156= 2 w^2+28 w+196}}}
     mve 1156 to the right
          {{{0 = 2w^2 +28w+196-1156}}}
            {{{ 0 = 2w^2+28w-960}}} 
       divide with 2 each and every term on both sides
           {{{ 0/2 = (2w^2/2) +28w/2-960/2}}}
             {{{0 = w^2+14w-480}}}
            {{{0 =w^2+30w-16w-480}}}
             {{{0 =w(w+30)-16(w+30)}}}
          {{{0 =(w+30)(w-16)}}}
        possible solution
            either (w+30)= 0 or (w-16)=0
                    w=-30      or w= 16
 w cannot be negative
hence w= 16 cm
 length  = 16+14 = 30 cm
Perimeter ={{{ 2(length+width)}}}
          ={{{2(30+16)}}}
          ={{{2(46)}}}
         = 92 cm
Result : Perimeter  = 92 cm