<PRE><B>Question 90472</B>


     One leg of a right triangle is 6 cm longer than the other leg. The length of the hypothenuse of the triangle is 18 cm. Find the length of the two legs?

  Let the length of the smaller leg be = x cm
   
     the length of the longer leg      = x+6  cm
   
                   hypotenuse          = 18 cm
 According to pythagorous theorem(hypotenuse)^2= (smaller leg )^2+(longer leg)^2
   

                        (18)^2 = x^2+(x+6)^2

                          324 = x^2+x^2+12x+36

                       2x^2+12x+36-324 = 0

                       2x^2+12x-288 = 0
       divide by 2 throughout

                      x^2+6x-144 = 0    since we cannot factorise 144 exactly we have to use the formula   x = -b+-sqrtb^2-4ac divided by 2a

     on simplifying we get x = -3+-sqrt 153.  

         the longer side  will be +3+-sqrt 153 </PRE>