Two positive numbers are in the ratio 7:11. If the sum of their squares is 13770, then the difference between the two numbers is:

Let the two positive numbers be 7x and 11x.
Given the sum of their squares is 13770:

(7x)
2
+(11x)
2
=13770
49x
2
+121x
2
=13770
170x
2
=13770
x
2
=
170
13770
​
=81
x=
81

​
=9
The difference between the two numbers is:

Difference=11x−7x=4x
Difference=4×9=36