Question 814762
   Let one side  =  x cm.  Then,

   Second side  =  x + 7 cm.

   Hypotenuse  =  17 cm.  (Given)

   According to the Pythagoras theorem,

   {{{17^2 = x^2 + (x+7)^2}}}
   
   =  {{{289 = x^2 + x^2 + 14x + 49}}}

   =  {{{289 = 2x^2 + 14x + 49}}}

   =  {{{2x^2+14x+49 = 289}}}

   =  {{{2x^2+14x = 289-49}}}

   =  {{{2x^2+14x = 240}}}  Dividing this equation by 2, we get

   =  {{{x^2+7x = 120}}}

   =  {{{x^2+7x-120 = 0}}}

   =  {{{(x+15)(x-8) = 0}}}.  So, either (x+15) or (x-8) = 0.

   So, x = -15  or x = 8.  But x cannot be equal to -15 as it is not a real No.

   So, {{{highlight(x = 8)}}}. So one side = 8 cm. and another side = 15.

   I think, it is clear to you now. All the best.  Feel free to contact me at   gsmani9@yahoo.com as I am a home tutor in India.