<PRE><B>Question 683731</B>
Let the sides of the triangle be a and b and the hypotenus be c.
From Pythagoras theorem,
a^2 + b^2 = c^2 
 =10^2 =100
Therefore,
a^2 + b^2 = 100.....(1)
Also,
area of the triangle =(1/2)absinc
20 =(1/2)absin90
20 =(1/2)ab * 1
Multiply through by 2
40 = ab.....(2) 
Now,
 (a+b)^2 = (a+b)(a+b)
=a^2 + 2ab + b^2
=(a^2 +b^2) +2(ab).
Now substitue the values in equations 1 and 2.
(a^2 +b^2) +2(ab) =
(100) + 2(40) =
100 + 80 =180</PRE>