Question 90473

 One leg of a right triangle is 12 cm longer than the other leg. The length of the hypotenuse of the triangle is 36 cm. Find the length of the two legs.

   Let the length of th smaller leg be = x  cm 
    
      the length of the longer leg     = x+12  cm 
      the length of the hypotenuse     = 36  cm

         According to Pythagorous theorem , (hypotenuse)^2 = sum of the squares of the other two sides

          (hypotenuse)^2 = (smaller leg)^2+ (longer leg)^2

                   (36)^2 = x^2+ (x+12)^2
                     1296 = x^2+x^2+24x+144

                     2x^2+24x+144-1296 = 0

                     2x^2+24x-1152 = 0
 divide by 2 throughout

                    x^2+12x-576 = 0   since the factors for 576 cannot be found

   use the formula x = -b+-sqrtb^2-4ac divided by 2a

                  we get x = -6+-sqrt 612

    the other length is 6+-sqrt 612