a + b + c = 42            (1)
a^2 + b^2 = c^2           (2)
a^2 + b^2 + c^2 = 722     (3)


From (2) and (3)


2c^2 = 722  ====>  c^2 = 722/2 = 361

c =  = 19.


Now substitute  c= 19  and  c^2 = 361 into eq(1)  and eq(2). You will get

a + b = 23           (1')
a^2 + b^2 = 361      (2')


Now square both sides of (1').  Keep (2') as is. You will get

a^2 + 2ab + b^2 = 23^2 = 529     (1'')
a^2 +       b^2 = 361            (2'')


Subtract  (2'')  from  (1'').  You will get

2ab = 529 - 361 = 168.



Now the area of the triangle =  =  = 42.    ANSWER