The perimeter of a rectangle is 50 centimeters. the length of the rectangle is one more than 3 times the width of the rectangle. what are the dimensions of the rectangle

Let's let w = width of the triangle. Let's also write the length in terms of w:
Length = 3w+1

The perimeter of the rectangle is 2l+2w=P

2(3w+1) + 2(w) = 50     [base equation]
6w+2+2w=50   [distribute the 2]
8w+2=50   [combine like terms]
8w=48   [subtract 2 from both sides]
w=6    [divide 8 from both sides]
Therefore, the width is 6 cm.
3(6)+1 is the length = 19 cm