the ratio of three number is 3:4:5and the sum of the theire square is 1250.The sum of the three number is ?

Question

the ratio of three number is 3:4:5and the sum of the   theire square is 1250.The sum of the three number is ?

anonymous · Answer

Let the numbers be 3x, 4x, 5x
Thus according to the question
$$(3x)^2 + (4x)^2 + (5x)^2 = 1250$$
i.e.  $$9x^2 + 16x^2 + 25x^2 = 1250$$
i.e. $$50x^2 = 1250$$
i.e. $$x^2 = \frac{1250}{50} = 25$$
i.e. $$x =\pm 5$$
Now if x=5 
Then first number =3x= 15
        second number =4x= 20
       Third number =5x= 25
Sum of numbers = 15+ 20 + 25 = 60