One side of a kite is 1 cm less than 4 times the length of another. if the perimeter is 38 cm, find the length of each side

We can use a system of equations to solve this.
Length 1 = x
Length 2 = y

Set up the system.
2x+2y=38
x+1=4y

Isolate the variable on one equation.
x=4y-1

Substitute that into the other equation.
2(4y-1)+2y=38

Solve.
8y-2+2y=38
10y=40
y=4

Substitute back into other equation.
x=4(4)-1=16-1=15

The lengths are 15 cm and 4 cm.

Hope this helps!