In the 3 by 5 flag, the 3 is the smaller side
The student has 3/5 = x/48 which is not correct.
This is because the x isn't the shorter side. Instead, it's the longer side.
The equation they should have set up is 3/5 = 48/x
Cross multiply and solve to get...
3/5 = 48/x
3x = 5*48
3x = 240
x = 240/3
x = 80
The longer side of the larger flag is 80 feet
I.e. the larger flag is 48 feet by 80 feet. It's similar to the 3 ft by 5 ft flag.