hello :
let : y The length and x the width .... the perimeter is : 2(x+y)
The length of a rectangle is one more than five times its width: y = x +5
the system is: 2(x+y) = 38.....(1)
y = x + 5.........(2)
subst in (1) : 2(x+x+5) = 38
4x+10 = 38
4x =28...... x = 7
but: y = x +5
y = 7+5 = 12