Three positive numbers are in the proportion 3 : 4 : 6. If the sum of their squares is 244, then what is  value of the largest number?

12

The proportion of three numbers = 3 : 4 : 6

The proportion of their squares = 9 : 16 : 36 

Given, 9r² + 16r² + 36r² = 244

                           61r²    = 244   

                           ⇒    r² = 4   or r = 2

The largest number in the proportion = 6r = 6 x 2 = 12