Question:
Find three numbers in the ratio 2:3:5, the sum of whose squares is 608.
Solution:
Let us assume the three number be 2a, 3a, 5a
Then,
Given, sum of squares of three numbers is 608
i.e. (2a)2 + (3a)2 + (5a)2 = 608
4a2 + 9a2 + 25a2 = 608
38a2 = 608
a2 = 608/38
a2 = 16
a = √16
a = √(4 × 4)
a = √(42)
a = 4
∴The numbers are, 2a = 2 × 4 = 8
3a = 3 × 4 = 12
5a = 5× 4 = 20