Answer is length of RU is 15
Step by step
To find height ( SU ) of the larger triangle we can use Pythagorean theorem a^2 + b^2 = c^2
We know a= 22 and c= 85
77^2 + b^2 = 85^2
5929 + b^2 = 7225
subtract 5929 from both sides to isolate variable
5929 - 5929 + b^2 = 7225 - 5929
b^2 = 1296
√b^2 = √1296
b = 36
Now we can find ( RU ) the leg of the smaller triangle
We know a= 36, c= 39
36^2 + b^2 = 39^2
1296 + b^2 = 1521
Subtract 1296 from both sides to isolate variable
1296 - 1296 + b^2 = 1521 - 1296
b^2 = 225
√b^2 = √225
b = 15
Length of RU is 15