Find three numbers in the ratio 2:3:5,

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