The ratio of three numbers is 3:5:4 and the sum of their squares is 11250. Find the sum of the numbers.

Let the three numbers be 3x, 5x, and 4x.
According to the question, the sum of their squares is 11250:

(3x)
2
+(5x)
2
+(4x)
2
=11250
9x
2
+25x
2
+16x
2
=11250
50x
2
=11250
x
2
=
50
11250
​
=225
x=
225

​
=15
The sum of the numbers is:

Sum=3x+5x+4x=12x
Sum=12×15=180