Given, the ratio of three positive numbers is 2:3:5. Let three numbers be 2a,3a and 5a. According to the question, (2a)2+(3a)2+(5a)2=1368 ⇒4a2+9a2+25a2=1368 ⇒38a2=1368 ⇒a2=
1368
38
=36 ⇒a=6 The numbers are 2×6,3×6 and 5×6 i.e., 12, 18 and 30 . Sum of the numbers =12+18+30=60 Hence, sum of the numbers is 60 .